Notice that the width of each rectangle is 1. The height of the left rectangle is found by plugging 1 into the
equation y = x^2 + 2 (yielding 3); the height of the right rectangle is found by plugging 2 into the same
equation (yielding 6). The combined area of the two rectangles is (1)(3) + (1)(6) = 9. So we could say
that the area under the curve is approximately 9 square units.
Naturally, this is a pretty rough approximation that significantly underestimates the area. Look at how
much of the area we missed by using two rectangles! How do you suppose we could make the
approximation better? Divide the region into more, thinner rectangles.
This time, cut up the region into four rectangles, each with a width of . It looks like the following: