Consider the integral \(\int_{C} y^{2} d x-2 x^{2} d y\). Evaluate this integral for the following curves:

a. \(C\) is a straight line from \((0,2)\) to \((1,1)\).

b. \(C\) is the parabolic curve \(y=x^{2}\) from \((0,0)\) to \((2,4)\).

c. \(C\) is the circular path from \((1,0)\) to \((0,1)\) in a clockwise direction.