Assume $f:\mathbb{R}\to\mathbb{R}$ is a Lebesgue integrable function and let $\phi:\mathbb{R}\to\mathbb{R}$ be a continuously differentiable bijection. Show that: $$\int_\mathbb{R} f\circ \phi|\phi'|dm=\int_\mathbb{R}f dm$$
I tried first considering the basic case that $f=\chi_E$, an indicator function. Then, $$\int_\mathbb{R} fdm=\int_\mathbb{R} \chi_E dm=m(E)$$. However I am stuck with how to evaluate the other side $\int_\mathbb{R} \chi_E \circ \phi|\phi'| dm=?$
Thanks for any help.