Let $\gamma:[a,b]\rightarrow\mathcal{H}$ be a curve that is continuous and piecewise $\mathcal{C}^1$. The hyperbolic length of $\gamma$ is defined by
$$\ell(\gamma) = \int_a^b \sqrt{B(\gamma'(t),\gamma'(t))}\,\mathrm{d}t.$$
Show that if $h:[c,d]\rightarrow[a,b]$ is a diffeomorphism, then $\ell(\gamma) = \ell(\gamma\circ h)$.