C is the segment of straight the point $\displaystyle (a,b)$ to point $\displaystyle (c,d)$. Calculate
$\displaystyle \int_C -ydx + xdy$
Green's Theorem states that
$\displaystyle \int_C{(L\,dx + M\,dy)} = \int{\int_D{\left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right)}}$
Where $\displaystyle C$ is a positively oriented, piecewise smooth, simple closed curve in the plane, and $\displaystyle D$ is the region bounded by $\displaystyle C$.
Here $\displaystyle L = -y, M = x$ so $\displaystyle \frac{\partial L}{\partial y} = -1, \frac{\partial M}{\partial x} = 1$.
But what is your region? All you've given is a straight line. What bounds the region $\displaystyle D$?