## Continuously differentiable with bounded derivative

Let f be a continuously differentiable function on [0,1] such that the least upper bound on [0,1] of |f'(x)|=M (a real number).

Prove that:

|(integral 0,1 of f(x)dx)-(sum of f(i/n)/n from i=1 to n)|<=M/n

Sorry; I don't know how to use math typesetting. Thanks!