(Solved): Use Green's Theorem to evaluate \[ \int_{C} \mathbf{F} \cdot d \mathbf{r} \] if \( \mathbf{F}(x, y) ...

Use Green's Theorem to evaluate \[ \int_{C} \mathbf{F} \cdot d \mathbf{r} \] if \( \mathbf{F}(x, y)=\left(e^{-x}+y^{2}\right) \mathbf{i}+\left(e^{-y}+x^{2}\right) \mathbf{j} \) and \( \mathrm{C} \) is the curve that consists of \( y=\cos x \) from \( \left(-\frac{\pi}{2}, 0\right) \) to \( \left(\frac{\pi}{2}, 0\right) \) and the line segment from \( \left(\frac{\pi}{2}, 0\right) \) to \( \left(-\frac{\pi}{2}, 0\right) \).