Solution
= Solution
The <velocity vector> of the <helix> is $r'(t)=(-\sin t,\cos t,1)$, whose <Euclidean norm> is $\sqrt2$. Thus its <arc length> over the stated parameter interval is
$$
\boxed{L=\int_0^{2\pi}\|r'(t)\|\,dt=2\pi\sqrt2.}
$$
Omitting the two endpoints does not change this finite <arc length>.