The Simpson's rule in calculus

Answer 1

That's a method used for numerical integration, i.e. for an approximate calculation of definite integrals.

Answer 2

The integral of a function f(x) with respect to x, over the interval (a, b) ish/3*[f(x0) + 4*f(x1) + 2*f(x2) + 4*f(x3) + ... + 4*f(xn-1) + f(xn)] where

x0 = a, xn = b and h = (b-a)/n.