We write f(b) - f(a) as the sum of the difference of f over many little intervals x_k - x_k-1

We apply the mean value theorem on each small interval

This yields, for some c_k in the kth interval for each k.

This is a Riemann sum for integrand f '(x), limits a and b, and variable of integration x, for any n.

By taking the limit as , we get