Counterexample to Fubini?
Consider the double integrals $$I:=\int_0^1\int_0^1{y-x\over(2-x-y)^3}\ dy\ dx\ ,\qquad J:=\int_0^1\int_0^1{y-x\over(2-x-y)^3}\ dx\ dy\ .$$ Then $$\int_0^1{y-x\over(2-x-y)^3}\ dy={y-1\over(2-x-y)^2}\Biggr|_{y=0}^1={1\over(2-x)^2}\ .$$ It follows that $$I=\int_0^1 {dx\over(2-x)^2}={1\over 2-x}\Biggr|_0^1={1\over2}\ .$$ Similarly you get $J=-{1\over2}\ne I$.