Distance and Arc Length

Find the length of the curve and the total change in position:

$\mathbf{r}(t) = \langle t^2, t, \frac{1}{3}t^3 \rangle$, $0 \leq t \leq 1$

$\mathbf{r}(t) = \langle t \sin t + \cos t, t \cos t - \sin t \rangle$, $\sqrt{2} \leq t \leq 2$

$\mathbf{r}(t) = \langle \cos t^2, \sin t^2, t^2 \rangle$, $0 \leq t \leq 3$