Does the AP test make distinction between these three ways? For example, will there be a free response that will say you have to use a certain method to estimate the area?
Yes. In the FRQs there will be one or two parts of the questions that ask you to calculate the area of a graph with riemann sums by using the left, right, midpoint, and trapezoidal methods. Often you cannot simply use the Rules and call it a day because the widths of the intervals may not be the same. But it is not difficult. Check this video: 2011 Calculus AB Free Response #2 (a & b) | Calculus | Khan Academy
