What is the sum of all the integers between -12.1 and 3.3?
The problem is asking for the sum of the integers from $-12$ to 3.  The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms.  The number of integers from $-12$ to 3 is $3 - (-12) + 1 = 16$, so the sum is $(-12 + 3)/2 \cdot 16 = \boxed{-72}$.