Answer
7/6
Work Step by Step
Expand the equation and integrate with respect to dx first:
$\int\int(x^2+2xy+y^2)dxdy$ with limits for both x and y from 0 to 1
$=\int[1/3\times x^3+x^2y+xy^2]dy$ with limits for both x and y from 0 to 1
$=\int1/3+y+y^2 dy$
Integrate with respect to dy and evaluate:
$1/3\times y+1/2\times y^2+1/3\times y^3$ with limits for y from 0 to 1
$=1/3+1/2+1/3=7/6$
