Answer
$0$
Work Step by Step
Green Theorem, Tangential form for Counterclockwise Circulation, can be defined as:
$\oint_C F \cdot T ds= \iint_{R} (\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}) \space dx \space dy $
Now, $$\oint_C F \cdot n ds= \iint_{R} \dfrac{\partial (x^2)}{\partial x}-\dfrac{\partial (y^2)}{\partial y} dx dy \\= \int_{0}^1 \int_0^{1-x} 2x-2y dx dy \\= \int_{0}^1 \int_0^{1-x} [2x-2y] dx dy \\= \int_{0}^1 4x-3x^2-1 dx \\=[2x^2-x^3-x]_0^1 \\=0$$
