Rectangle Method Example

This example was used in class to help introduce the basics of the Rectangle Method.
What happens to the approximate area when you increase the number of subintervals (rectangles)? What point (left, midpoint or right) gives the most accurate approximation? (Try each type of point and increase the value of n until you get the best approximation). Are there other shapes than rectangles that you think might be more accurate using smaller number of partitions?