Answer
5/2-1/e
Work Step by Step
Integrate with respect to dx first:
$\int[1/2\times x^2+xe^{-y}]dy$ with x limits from 1 to 2
$=\int[2+2e^{-y}-1/2-e^{-y}]dy$
$=\int(3/2+e^{-y})dy$
Integrate with respect to dy:
$=3/2\times y-e^{-y}$ with y limits from 0 to 1
$=3/2-1/e-(0-1)=5/2-1/e$
