Triple Integral - Simple one

Hey there, I'll be delighted to get some help in the following question:

Let A be the region in space bouded by the next planes:

$\displaystyle x=1$, $\displaystyle x=2$, $\displaystyle x-y+1=0$,

$\displaystyle x-2y=2$, $\displaystyle x+y-z=0$ , $\displaystyle z=0$...

Write the integral $\displaystyle \int \int \int_{A} f(x,y,z) dxdydz $ as shown in the next theorem:

Let E be a closed region with a surface in R^2 and let [tex] g^1, g^2[tex] be two real functions, continous in E. Let's look at A:

$\displaystyle A=( (x,y,z)|(x,y) \in E, g^1(x,y)\leq z \leq g^2(x,y) $. Then if f is a continous function with 3 variables, continous in A, then:

$\displaystyle \int \int \int_{A} f(x,y,z) dxdydz = \int \int_{E} (\int_{g^1(x,y)}^{g^2(x,y)} f(x,y,z)dz) dxdy $...

The problem is I can't figure out how the region A looks like...

Hope you'll be able to help me dealing with this question...

Thanks in advance