on how to prove this problem. I don't know where to start. Any help is very much appreciated.

Suppose that a function f: [a,b] >> R is bounded and P = {x_0,x_1,...,x_n} is a partition of [a,b]. Then there exist 2 real numbers m and M such that

m(b-a) <= L(P,f) <= S(P,f) <= U(P,f) <= M(b-a)

for any c_k in [x_k-1,x_k]