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