If the vector field is $\displaystyle \vec{F}=xy\vec{i}+yz\vec{j}+zx\vec{k}$

How do you calculate $\displaystyle \int^{}_{C}\vec{F}\cdot d\vec{r}$ where $\displaystyle C$ is the polygonal path from $\displaystyle (1,0,0)$ to $\displaystyle (0,1,0)$ to $\displaystyle (0,0,1)$ by parametrizing each segment.