Regarding the word ESTIMATE: You are not being asked to make a guess. You still need to compute. Of course, the area using rectangles is an approximation of the actual area under f(x).

Sketch the remaining rectangle. Notice: The height of the LAST rectangle is evaluated at x = 2 (not x = 3).

Each rectangle has a base of 1 and a height of f(x). Area = 1(f(−3) + f(−2) + f(−1) + f(0) + f(1) + f(2)) =_____________

Notice: The height of the FIRST rectangle is evaluated at x = −2. The height of the LAST rectangle is evaluated at x = 3.

Each rectangle has a base of 1 and a height of f(x). Area = 1( f(-2) + f(-1) + f(0) + f(1) + f(2) + f(3)) =_____________

The trapezoidal sum is the AVERAGE of the left- and right-endpoint sums! Expain why this happens (algebraically and geometrically).