Volume of A Solid I wonder if some one can clarify the confusion I have over the following problem:
Find the volume of the solid bounded by the parabolic cylinder $z = 1- y^2$, the planes $x = 0, z = 0$ and the plane $x+z = 1$. My struggle is to visualize the solid and find the set up of the triple integral for the volume. 
What is your approach?

The solid is bounded by the graph of the plane $x(y,z)=1-z$ over the domain in the $yz$-plane given by the parabolic segment 
$$D=\{(0,y,z)\,:\; 0\leq z\leq 1-y^2, y\in [-1,1]\}.$$ 
Therefore
$$\mbox{volume}(D)=\iint_D (1-z) dydz=\int_{y=-1}^1\left(\int_{z=0}^{1-y^2}(1-z)dz\right) dy=\frac{4}{5}.$$
