\[\iint_{S}\left(\frac{\partial F_{2}}{\partial x}-\frac{\partial F_{1}}{%
\partial y}\right)\,\mathrm{d}A=\int_{C}\mathbf{F}\cdot\,\mathrm{d}\mathbf{s}=%
\int_{C}F_{1}\,\mathrm{d}x+F_{2}\,\mathrm{d}y.\]