# Chain rule with measures

Suppose that $F$ is continuous and increasing on [a,b], with $F(a)=c, F(b)=d$. Suppose that $f$ is integrable, show that
$\int_c^df(y)dy=\int_a^bf(F(x))\mu_F(x)$ where $\mu_F((x,y])=F(y)-F(x)$
So far I have shown that $m(E)=\mu_F(F^{-1}(E))$ for Borel sets $E$, but I don't see how this helps.