Сhange the order of integration in the double integral

Question

I have to change the order of integration in this double integral

I've decided to divide it in two similar areas D1 and D2

And I've got the following result

Can You chech it and state my probable mistakes. I have to be sure that the result is correct. Thanks

Answer 1

$$\{(x,y)\mid0\lt x\lt1,x-1\lt y\lt1-x\}=\{(x,y)\mid x+|y|\lt1\}$$ $$\int_0^1\mathrm dx\int_{x-1}^{1-x}f(x,y)\mathrm dy=\int_{-1}^1\mathrm dy\int_0^{1-|y|}f(x,y)\mathrm dx$$