Curves $C_1$ and $C_2$ are parametrized as follows: $$C_1 \mbox{ is } (x(t),y(t)) = (0,t)\quad\mbox{ for } -1\le t\le1$$ and $$C_2 \mbox{ is } (x(t),y(t)) = (\cos t,\sin t) \quad\mbox{ for } \pi/2 \le t\le 3\pi/2.$$ Sketch, on a separate sheet of paper, the curves $C_1$ and $C_2$ with arrows showing their orientation.

Next, suppose that $\vec F = (5 x + 3 y)\,\vec i + 6 y\,\vec j$. Calculate $\int_C\vec F\cdot d\vec r$, where $C$ is the curve given by $C=C_1+C_2$.
$\int_C\vec F\cdot d\vec r =$