Interpolatory Quadrature

Abstract

It is well-known that if the anti-derivative F of a given function $f \in C[a,b]$ is available, thenthe definite integral of f on $[a,b]$ can be evaluated by applying the fundamental theorem ofcalculus, namely:$\int\limits_{a}^{b} {f(x)dx\; = \;F(b)\; - \;F(a)} Z$.Unfortunately, with the exception of only a handful of functions f , it is not feasible tofind their anti-derivatives F.