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We can easily set up a spreadsheet to evaluate a given integrand f at a large number of points in the range from a to b, and to form Riemann sums. A symmetric way to do this is the "trapezoid rule" that approximates the area in a strip by the area in the trapezoid with the same height at either end of the given interval. We explore this rule and more accurate extrapolations. The first of these is called Simpson's rule.
25.1 The Trapezoid Rule
25.2 Simpson's Rule
25.3 Extrapolations and Better Approximations