1. An approximation formula for definite integrals which states that the integral of a real-valued function f on an interval [a,b] is approximated by (3/8)h[f (a ) + 3f (a + h ) + 3f (a + 2h ) + f (b )], where h = (b - a )/3; this is the integral of a third-degree polynomial whose value equals that of f at a, a + h, a + 2h, and b.

2. A method of approximating a definite integral over an interval which is equivalent to dividing the interval into equal subintervals and applying the formula in the first definition to each subinterval.