The curve $C$ is given by

$$\mathbf{r}(t)=\left(\sqrt{2} e^{t},-e^{t} \sin t, e^{t} \cos t\right), \quad-\infty<t<\infty$$

(i) Compute the arc length of $C$ between the points with $t=0$ and $t=1$.

(ii) Derive an expression for the curvature of $C$ as a function of arc length $s$ measured from the point with $t=0$.