Computing the CDF from a PDF 
I understand how to find the CDF of Y it would be negative infinity to y for the bounds, but I am stuck since I am given two functions. 
Any help would be appreciated 

Since $\int_{-1}^0\tfrac{-\pi}{8}\sin(\pi y)dy=[\tfrac18\cos\pi y]_{-1}^0=\tfrac14$, $\frac{3}{4c}=\int_0^1\sin(\pi y)dy=\frac{2}{\pi}\implies c=\frac{3\pi}{8}$. So the CDF $F_Y(y)$ increases from $0$ at $y-1$ to $\tfrac14$ at $y=0$ and $1$ at $y=1$, and is given by$$F_{Y}\left(y\right)=\left\{ \begin{array}{rl}
0 & y\le-1\\
\frac{1+\cos\pi y}{8} & y\in\left[-1,\,0\right]\\
\frac{5-3\cos\pi y}{8} & y\in\left[0,\,1\right]\\
1 & y\ge1
\end{array}\right..$$
