Fix DataFrame.info() range summary for DatetimeIndex
**Fix `DataFrame.info()` range summary for DatetimeIndex**

This PR aims to provide better description of [DatetimeIndex](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DatetimeIndex.html) within [DataFrame.info](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.info.html) in relation to the display of the range of unsorted indexes, by replacing the original first to last element values with "min date" to "max date" values.

Fixes https://github.com/pandas-dev/pandas/issues/31116

<del>
This PR fixes range display errors that might occur when [DataFrame.info](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.info.html) describes a [DatetimeIndex](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DatetimeIndex.html) of big dataframes: depending on the dataframe structure, related *"min date" to "max date"* values can be wrong.

Example of output produced by `DataFrame.info()`:

```python
import pandas as pd
idx = pd.date_range('2020-01-15 01:03:05',
                    periods=1000004, freq='ms')
df = pd.DataFrame({'count': range(len(idx))}, index=idx)
df
df.info()
```

`df` output:
```
                           count
2020-01-15 01:03:05.000        0
2020-01-15 01:03:05.001        1
2020-01-15 01:03:05.002        2
2020-01-15 01:03:05.003        3
2020-01-15 01:03:05.004        4
...                          ...
2020-01-15 01:19:44.999   999999
2020-01-15 01:19:45.000  1000000
2020-01-15 01:19:45.001  1000001
2020-01-15 01:19:45.002  1000002
2020-01-15 01:19:45.003  1000003
```

`df.info()` output:
```
<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 1000004 entries, 2020-01-15 01:03:05 to 2020-01-15 01:19:45.003000
Freq: L
Data columns (total 1 columns):
count    1000004 non-null int64
dtypes: int64(1)
memory usage: 15.3 MB
```

This PR fixes possible errors within the description: `"DatetimeIndex: ... entries, `*date_a*` to `*date_b* output, where *date_a* and *date_b* should respectively show minimum and maximum date range values.
</del>
Thanks for your PR, and welcome :)

I'm not sure I see the issue in your example - `df.info()` shows 
```
2020-01-15 01:03:05 to 2020-01-15 01:19:45.003000
```
but isn't that what we were expecting to see?

Could you please raise an issue first, in which you show an example of where the output is wrong, along with your expected output? Please add test(s) for the issue you are trying to fix - we typically ask for these as the first part of any PR Ok, thanks. I'll first create an issue and relate it to this PR. Thanks for opening the issue.

However, before this PR can be accepted, you need to write tests / make sure you don't break existing ones - see [contributing to the code base](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#contributing-to-the-code-base):

> pandas is serious about testing and strongly encourages contributors to embrace test-driven development (TDD). This development process “relies on the repetition of a very short development cycle: first the developer writes an (initially failing) automated test case that defines a desired improvement or new function, then produces the minimum amount of code to pass that test.” So, before actually writing any code, you should write your tests. Often the test can be taken from the original GitHub issue. However, it is always worth considering additional use cases and writing corresponding tests.
> 
> Adding tests is one of the most common requests after code is pushed to pandas. Therefore, it is worth getting in the habit of writing tests ahead of time so this is never an issue. @WillAyd just checking - is this something pandas would like to support?

If so, @Ircama , is this something you're still working on? On a second thought, I think I might prefer the current behaviour. Otherwise, if I did `df.info()` and saw the min and max values instead of the first and last ones, I might get the (possibly false) impression that my index was already sorted > On a second thought, I think I might prefer the current behaviour.

Yes, I did some further analysis and at the end I agree.

Even if the wording used with `df.info()` on *DatetimeIndex* entries might lead to believe that the two shown elements are the index range, actually these are the first and the last element of the DataFrame index.

Sorting the index is optional and the shown values could help the developer check whether sorting has been applied to the index.

I would then consequently close https://github.com/pandas-dev/pandas/pull/31069 and https://github.com/pandas-dev/pandas/issues/31116.

Thanks for the support so far.