Answer
$-2$
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 $
$$\oint_C F \cdot n ds= \iint_{R} \dfrac{\partial (2x)}{\partial x}-\dfrac{\partial (3y)}{\partial y} \space dx dy \\= \int_{0}^1 \int_0^{1-x} [2-3x] \space dx \space dy \\= -\int_{0}^{\pi} \int_0^{\sin x} \space dy \space dx \\= -\int_{0}^{\pi} \sin x dx \\ =[\cos x]_0^{\pi} \\=-2$$
