The curve $\gamma$ is the intersection between the cylinder $x^2+y^2=1$ and the plane $z=2-x$, so $$\gamma(t)=(\cos(t),\sin(t),2-\cos(t)),\quad 0\leq t\leq2\pi$$
I have to evaluate its mass, with density function $$\delta(x,y,z)=y^2$$
What I did was $$\gamma'(t)=(-\sin(t),\cos(t),\sin(t))\Rightarrow||\gamma'(t)||=\sqrt{1+\sin^{2}(t)}$$ Hence, the mass $m$ is $$m=\int_{0}^{2\pi}\sin^{2}(t)\sqrt{1+\sin^{2}(t)}dt$$
I have no clue how I could evaluate this integral, and, to be honest, I just need the final answer. However, I tried using Wolfram Alpha and it's not what I'm looking for.
My question: is the formula for $m$ correct?