Let , $f$ be a continuously differentiable real-valued function on $[a,b]$ such that $|f'(x)|\le k $ for all $x\in [a,b]$. For a partition $P=\{a=a_0<a_1<a_2<\cdots <a_n=b\}$ let $U(P,f)$ and $L(P,f)$ denotes the upper and lower Riemann sums of $f$ with respect to $P$. Then ,
(A) $|L(P,f)|\le k(b-a)\le|U(P,f)|$
(B) $U(P,f)-L(P,f)\le k(b-a)$
(C) $U(P,f)-L(P,f)\le k||P||$ , where $||P||=\max_{0\le i\le n-1}(a_{i+1}-a_i)$
(D) $U(P,f)-L(P,f)\le k||P||(b-a)$
I really can't understand how I utilize the condition $|f'(x)|\le k$ ?
Can anyone give me any hint ?