Well, think about the interval from, well, this is a pretty straightforward one, the open interval from three to five. The function is here when x is equal to three, but if we wanted to get to five, it looks like we're asymptoting, it looks like we're asymptoting up towards infinity, and we just keep on going for a very long time, and then we would have to pick up our pencil and jump over, and then we would come back down right over here, and so here, we are not continuous over that interval. So now let's think about the more, the slightly more involved interval, the slightly more involved case is when you have a closed interval. F is continuous over the closed interval from a to b, so this includes not just the points between a and b, but the endpoints as well, if and only if f is continuous over the open interval and the one-sided limits, let me write this, and the limit as x approaches a from the right of f of x is equal to f of a, and the limit as x approaches b from the left of f of x is equal to f of b. Now what's going on here? Well, it's just saying that the one-sided limit when you're operating within the interval has to approach the same value as the function. So for example, if we said the closed interval from negative seven to negative five, well, this one is still reasonable, just based on the picking up your pencil thing, you don't have to pick up your pencil, and what you would do is at the endpoint, and at negative seven, this function is just plain old continuous, but if it wasn't defined over here, it could still be continuous because you would do the right-handed limit towards it, and you'd say, okay, the right-handed limit is equal to the value of the function, and then at this endpoint, at the second endpoint, you'd say, okay, the left-handed limit is equal to the function, even if it wasn't defined here, even if the two-sided limit were not defined.