Bounds of double integrals determined by a minimum

Question

I'm studying for exams and in the previous years there has been a question on a double integral where the domain has the condition : $ |y| <= min(1,2-x) $ My problem is that I don't understand how to use that because since $ x >= 0 $ there will two differents cases for y, one when x is between 0 and 1 and then when x is over 1 no ?

Any help is appreciated, Thanks in advance

Answer 1

If, as you wrote, $x\geq 0$ the integration area is the following