I curently have started reading differential geometry from these notes http://www.matematik.lu.se/matematik...igma/Gauss.pdf and I am trying to solve the exercise 2,7 which says:

Let the positively oriented $\displaystyle \gamma : \mathbb{R} \rightarrow \mathbb{R}^2$ parametrize a simple closed curve by arclength. Show that if the period of $\displaystyle \gamma$ is $\displaystyle L>0$ then the total curvature satisfies $\displaystyle \int\limits_0^L k(s)ds = 2 \pi$.

Any idea?