Write a C program that will calculate an approximate value for the definite integral of a curve using each of the two methods, the rectangle rule and the trapezoidal rule. Hopefully well be able to observe how the approximate value improves as we increase the number of sub-intervals (decrease the size of the sub-intervals).

At the minimum, your program should have separate functions for: (a) the calculation of a single rectangle; (b) the calculation of a single trapezoid; and (c) the calculation of f(x) for some x. (Of course, writing other functions for specific tasks is always encouraged.)

For our initial values, lets let NUM_INTERVALS = 100, and f(x) = x3 - 3x2 + 2. A diagram of that curve is depicted below. There are several opportunities to integrate that curve within [~0.3, ~2.3]. Have the computer ask the user which method he would like to use to do the integration, i.e., rectangle or trapezoid, and then to specify the endpoints. Your program will then return the result of the integral approximation based on the indicated method.