Evaluate the line integral $\oint_C \vec{F} \cdot d\vec{r}$ where $\vec{F} = \langle y + e^{\sin x}, x + \cos(y^2) \rangle$ and $C$ is the boundary of the region $D = \{ (x, y) : 0 \le x \le 1, 0 \le y \le 1 \}$ oriented counter-clockwise.