Question: Riemann sum approximation

Write a procedure approxInt that takes in a function f, a number of intervals
N, a left endpoint a, and a right endpoint b. Given these data, the procedure should split the
interval [a, b] into N subintervals and use the function f to estimate the area under the curve
(a) Left endpoints,
(b) Right endpoints,
(c) Midpoints, and
(d) Trapezoids.

 Write another procedure called compareApproxInt that does the following:
  (a) Takes as inputs the function f, the endpoints a and b, and the number of subintervals N.
  (b) Calls the procedure approxInt in order to estimate the area under the curve of f(x) with
       N subintervals, with the four different approximations methods.
  (c) Returns four sentences:
       Using        , the approximate area under f is        . This method has a margin of error of         .

Test compareApproxInt with the functions 
 f1(x) = x
 f2(x) = x^2 ,
 f3(x) = x^3 - 4 · x^2 , and
 f4(x) = e^x ,
 each on the interval [-1, 1], with 10 subintervals.


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