Integration problem in real analysis Let $f: [a,b]\rightarrow \mathbb{R}$ be a function, and let $m$=inf{$f(x)|x\in [a,b]$}, $M$=sup{$f(x)|x\in[a,b]$}.
Prove that for any partition $P$ and sample set $S$, $m(b-a)\leq RS(f,P,S)\leq M(b-a)$.
My attempt: $RS(f,P,S)=f(s_1)\Delta x_1 + ... + f(s_n)\Delta x_n$ ; $m(\Delta x_1 + ... + \Delta x_n)\leq f(s_1)\Delta x_1 + ... + f(s_n)\Delta x_n$.
Then what do I do?  

ANOTHER HINT: $$\Delta x_1+\ldots+\Delta x_n=b-a$$
