User:Spewin

Given the a polynomial

$f(x)=\Sigma _{i=0}^{n}p_{i}x^{k}$

The definite integral of f(x) is

$\int _{a}^{b}f(x)dx=\Sigma _{i=0}^{n}p_{k}{\frac {b^{k+1}-a^{k+1}}{k+1}}$

how do I factor out a (b-a) term so that I can find f(c) where for a < c < b, $\int _{a}^{b}f(x)dx=F(b)-F(a)=f(c)(b-a)?$