Answer
$\dfrac{3}{2}$; $\dfrac{-1}{2}$
Work Step by Step
Flux=$\iint_{R} (\dfrac{\partial M}{\partial x}+\dfrac{\partial N}{\partial y}) dx dy $ ...(1)
Equation (1) becomes $flux= \iint_{R} (\dfrac{\partial (2xy+x)}{\partial x}+\dfrac{\partial (xy-y)}{\partial y}) dx dy$
This implies that $flux=\int_{0}^1 \int_{0}^1(2y+x) dx dy=\dfrac{3}{2}$
Now, the tangential form for Green Theorem is given as:
Counterclockwise Circulation: $\oint_C F \cdot T ds= \iint_{R} (\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}) dx dy $
This implies that $\iint_{R} (y-2x) dy dx=\int_{0}^1 \int_{0}^1(y-2x) dx dy=\dfrac{-1}{2}$
