Suppose that F is a function that defines this way:

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$F:=F_{x}\overrightarrow{i}+F_{y}\overrightarrow{j}$

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and suppose u and V are vectors such that u $ =\left( u_{x}, u_{y} \right) $ and $\overrightarrow{V} = \dfrac{\partial F}{\partial u_{x}}\overrightarrow{i} + \dfrac{\partial F}{\partial u_{y}}\overrightarrow{j}$

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Is it true to say that $\displaystyle\iint_A \overrightarrow{\nabla}.\left( \delta u \right) dA$ $= \displaystyle\int_0^b \left[ \dfrac{\partial F}{\partial u_x} \right]_{x=0}^{x=a} dy$ $+\displaystyle\int_0^a \left[ \dfrac{\partial F}{\partial u_y} \right]_{y=0}^{y=b} dx$?

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if not, then what is the amount of LHS?