Answer
Outward flux $=2$ and Counterclockwise Circulation =0
Work Step by Step
Green's Theorem Normal form for outward Flux is: $=\oint_C F \cdot n ds= \iint_{R} (\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}) \space dx \space dy$
or, $= \iint_{R} (\dfrac{\partial (x-y)}{\partial x}-\dfrac{\partial (y-x)}{\partial y}\space dx \space dy$
or, $=2 \iint_{R} dx dy $
or, $=2$
Green Theorem -Tangential form for Counterclockwise Circulation is:
$\oint_C F \cdot T ds= \iint_{R} (\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}) \space dx \space dy$
$= \iint_{R} \dfrac{\partial (y-x)}{\partial x}-\dfrac{\partial (x-y)}{\partial y} dx dy$
or, $=\iint_{R} -1 -(-1) \space dx \space dy=0 $
