Origin of Double Integral Formulas for Volumes from Corral's Vector Calculus $\iint 1 - f(x,y)da$?

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Dear all I've been studying with Michael Corral's Vector Calculus book and in the Change of Variables part whenever he has a two variable function z = f(x,y) and we want to compute the volume of under the surface with z bound from 0 to 1. He uses the integral $\iint_R(1-z)dA$. I find the rest fairly intuitive but I've not been able to figure out why he starts with $1-z$ everytime. I do not think it's explained earlier. (I've read it multiple times, but to be fair I have a reading disability).

Could someone explain this to me?

Thank you very much!

I'm sure I'm missing something very obvious here. Apologies in advance!