Find volume of an object $y=1-x^2$ $\ldots$

Question

The $X$ and $Y$ axis, and curve $y=1-x^2$ define an area $\mathbf{A}$ from the first quarter of an $XY$ plane ($x \text{ and } y \ge 0$). An object is directly above $\mathbf{A}$ between planes $z=1$ and $z=2-y$. What is the volume of the object?

My apologies for the bad english, I hope I made myself understood. I'm in a bit of a hurry and would grately appreciate any help you could give me.

Answer 1

$$V=\int_0^1\int_0^{1-x^2}\!\!\!\!\int_1^{2-y}dz\,dy\,dx$$