> 
> Let C be a simple closed curve in a region where Green's Theorem holds. Show that the area of the region is:
> 
> 
> \begin{equation}
> A=\int\_{C}xdy=-\int\_{C}ydx
> \end{equation}
> 
> 
> 

Green's theorem for area states that for a simple closed curve, the area will be $A=\frac{1}{2}\int\_{C}xdy-ydx$, so where does this equality come from?