Given the a polynomial
f ( x ) = Σ i = 0 n p i x k {\displaystyle f(x)=\Sigma _{i=0}^{n}p_{i}x^{k}}
The definite integral of f(x) is
∫ a b f ( x ) d x = Σ i = 0 n p k b k + 1 − a k + 1 k + 1 {\displaystyle \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, ∫ a b f ( x ) d x = F ( b ) − F ( a ) = f ( c ) ( b − a ) ? {\displaystyle \int _{a}^{b}f(x)dx=F(b)-F(a)=f(c)(b-a)?}
