That's just a double integral. You're integrating from the x-y plane up to the surface that is . That's the z-direction. And we're integrating that over the foot-print in the x-y plane that's just the two unit squares underneath the surface which because it's symmetric, just multiply by two, the volume underneath the unit square as x goes from 0 to 1 and y goes from 0 to one or:

or if you wanna' be a purist, a triple integral:

but same dif.