Question 1003297
First sketch f(x) on the xy-plane and label the points (-pi/2, 0), (0,0), (0, pi/3), and (0,pi/2) (corresponding to the points in P).


To approximate the integral using the midpoint Riemann sum, for each "interval" bounded by consecutive points in P, take the midpoint and evaluate f at that x-value. This becomes your "height" of the rectangle. Multiply by the width of the interval.


For example, for the interval bounded by -pi/2, 0, we would want to take -pi/4 and compute f(-pi/4). Then we multiply f(-pi/4) by pi/2 (the width of the interval). Repeat for the other intervals and add.