Let $\displaystyle f(x) : [a,b] -> R$ be a bounded function such that $\displaystyle U(f,P) = L(f,P)$ for any partition P of [a,b].

Prove that there exists a constant c such that $\displaystyle f(x) = c$ for any x in [a,b] (by contradiction) .

Appreciate if someone could help on this one. Thanks...