Approximation of area under a curve

This shows how we can use upper and lower sums to approximate the area under the curve. Use the slider [i]n[/i] to change the number of rectangles used to calculate the upper and lower sums.

What happens when [i]n[/i] is (a) small, (b) large? Can you think of any way that we can make our approximation of the area under the curve more accurate?