Let \(C_{R}\) be the circle of radius \(R\) centered at the origin. Use the general form of Green's Theorem to determine \(\oint_{C_{2}} \mathbf{F} \cdot d \mathbf{r}\), where \(\mathbf{F}\) is a vector field such that \(\oint_{\mathcal{C}_{1}} \mathbf{F} \cdot d \mathbf{r}=9\) and \(\frac{\partial F_{2}}{\partial x}-\frac{\partial F_{1}}{\partial y}=x^{2}+y^{2}\) for \((x, y)\) in the annulus \(1 \leq x^{2}+y^{2} \leq 4\).