What is
would the solution be ?
If 0<=x<=1 and 0<=y<=1 and taking into account that x-y>1/2 can be expressed as y<x-1/2, then the intervals in which you have to integrate the density functions are 1/2<=x<=1 and 0<=y<=x-1/2, so... your answer is not correct.
In your answer, check x=0 and y=1/2... it does not satisfy x-y>1/2 because 0-1/2<1/2.
It is a good practice to graph the intervals and draw the line which represents x-y=1/2. Then, you paint the area for x-y>1/2.
Hope this helps.
Regards,
Federico.
Federico.