Let $\displaystyle f$ be a continuous function over a curve $\displaystyle C$ parametrized by $\displaystyle [a,b]\to C$.

If $\displaystyle \gamma ^-(t):[c,d]\to C$ is a reparametrization of $\displaystyle \gamma$ that inverts the orientation, show that $\displaystyle \int _{\gamma ^-} f(z) dz = - \int _{\gamma} f(z)dz$.

My attempt : I still didn't find the main idea of the proof. Stuck at starting. I think I've seen a similar proof in calculus 3, but I don't remember it.