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)

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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.