$C_1$ and $C_2$ start at $(-1,1)$ and end at $(1,-1)$. $C = C_2 - C_1$.
So I believe the radius of the semicircle is $1$, its circumference is $2\pi / 2 = \pi$, and its area is $\pi / 2$. If I'm wrong about any of that, then that will explain my confusion.
But assuming that's all right, I want to calculate the following:
$$\int_{C} \vec G \cdot d\vec r $$
I think I can use Green's Theorem: curl $\vec G = -6$, and the area of the semicircle is $\pi / 2$, so the $\int_{C_1} \vec G \cdot d\vec r$ should evaluate to $-3\pi$, right? Yet my textbook says the answer is $-6\pi$. Can you see why?
Just to be absolutely sure I'm not misinterpreting the question, I've pasted it in here so you can confirm for yourself:
