According to the integral, your region of integration is bounded by:

1. the plane z=0

2. the plane z=1-y

3. the surface y=sqrt(x), and

4. the plane x=0

(that means your diagram is wrong, though)

So I think the limits would be:

y from sqrt(x) to 1-z

z from 0 to 1-sqrt(x)

x from 0 to 1

- Hollywood