Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1)$. The value of the line integral
$$ \oint_{C}\left(-e^{y} d x+e^{x} d y\right)$$
is
- $e^{2}+2 e-3$
- $e^{2}-2 e-3$
- $e^{2}+e-1$
- $e^{2}+e+1$
