(c) Consider the following theorem. If f is integrable on [a, b], then Use this to evaluate the integral. 5.33 [* f(x) dx = lim f(x) Ax, where Ax = b-a and x, = a + iAx. 111 (d) Interpret the integral in part (c) as a difference of areas. i-1 n O The integral represents the area below the x-axis minus the area above the x-axis. O The integral represents the area above the x-axis minus the area below the x-axis. Illustrate with a diagram. y 9 8 7- 6 5 4 3 2 1 10 5 9 4 8 3 2 6 1 5 4 -1 3 -2 2 -1 3 5 -3- -2 -4 O-3L 2 O-14 y 9r 8 7- 6- 5 4 3 2 -1 2 3 -2 5 0-31