# Please explain how to do this proof ?

I would appreciate if somebody could help me with the following problem:

Please explain how to do this proof ?  $G(x)$ : monotone increasing function and $G(x)\geq 0$ , $G'(x),f(x)$ : conti-function on $[a,b]$ then exist $c\in (a,b)$ s.t $$\int_{a}^{b}f(x)G(x)dx=G(a)\int_{a}^{c}f(x)dx$$

-
Is this correct? What if $G(a)=0$? Take $f(x)=g(x)=x$ and $[a,b]=[0,1]$. –  Maesumi Feb 20 '13 at 12:34
We do have $\int_a^b f(x)g(x)dx= g(c)\int_a^bf(x)dx$ though. –  Maesumi Feb 20 '13 at 12:36