Some computer algebra systems have commands that will draw approximating rectangles and evaluate the sums of their areas, at least if x*1 is a left or right endpoint. (For instance, in Maple use leftbox, rightbox, leftsum, and rightsum.)
(a) If f(x) = 1/(x2+1), 0 ≤ x ≤ 1, find the left and right sums for n = 10, 30 and 50.
(b) Illustrate by graphing the rectangles in part (a).
(c) Show that the exact area under f lies between 0.780 and 0.791.