Integral using Cauchy Schwarz inequality

Question

I'm trying to show that $$\int_a^b \left\|\frac{d\mathbf{r}(t)}{dt} \right\| \ dt = \|\mathbf{r}(b)-\mathbf{r}(a) \| $$ but I'm unsure of how to deal with the integral and the derivative of $\mathbf{r} $. Here $\mathbf{r} : \mathbb{R}\rightarrow \mathbb{R}^n $ is a vector valued function of t.