$\operatorname{Length}(\gamma)\neq \int_0^1\|\dot{\gamma}(t)\|\,dt$ possible?

Question

Let $\gamma:[0,1]\to\mathbb{R}^d$ be a rectifiable curve and define the length of the curve as $$\operatorname{Length}(\gamma)=\sup\left\{\sum\limits_{k=0}^{n-1}\|\gamma(t_{k+1})-\gamma(t_k)\|,n\ge 1, 0=t_0<t_1<\ldots<t_n=1 \right\}.$$ Is there an example where $\operatorname{Length}(\gamma)\neq \int_0^1\|\dot{\gamma}(t)\|\,dt$ (assuming this quantity is well defined)?