10. (10 points) Evaluate $\int_L \vec{F}\cdot d\vec{r}$, where

$$\vec{F}=(4x+5y,e^{\cos y}+7x)$$

and $L$ is the path from $A$ to $B$, to $C$ to $A$ and to $D$ as shown below:

Note: The path from $B$ to $C$ is circular.