User:Spewin

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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)?