In a previews question I asked here I used the following definition of path length:$\gamma=(x(t),y(t),z(t))$ : $L(\gamma)=\intop_{a}^{b}\sqrt{(x'(t))^{2}+(y'(t))^{2}+(z'(t))^{2}}$.
In the answer another definition was used:
$ l(f)= \sup_{P}\sum_{i=0}^k |f(t_{i+1})-f(t_i)| $ where $f:[0,1]\to \mathbb{R}^3$, $f(0)=a$, $f(1)=b$ and the $\sup$ is taken over all partitions $P$ of $[0,1]$.
How can I show they are equivalent ?