$$ \int_0^1 (x+y) \,dx \,dy \nonumber $$ $$ \int_0^1 \left[ \frac{x^2}{2} + xy \right]_0^1 dy \nonumber $$ $$ \int_0^1 \left( \frac{1}{2}+y \right) dy \nonumber $$ $$ \left[ \frav{y}{2} + \frac{y^2}{2} \right]_0^1 \nonumber $$ $$ \frac{1}{2}+\frac{1}{2}=1