Evaluating the Integral ∫∫xexy dxdy from 0≤x≤1, 0≤y≤1

[says]

Homework Statement

∫∫xe^xy dxdy where upper and lower limits are 0≤x≤1, 0≤y≤1
so I complete u substitution and get the integral
1/y² ∫ u*e^u du
Now with integration by parts I end up with
xy*e^xy-e^xy/y²
I have to evaluate this integral at 0≤x≤1, 0≤y≤1, as mentioned above.
The problem I have is that after evaluating I get an answer of 1, but I've computed this question into symbolab online and it says the answer is e-2.
I was wondering how these two statements are equivalent (below)
(e^y(y-1)+1)/y²

(e^y - (e^y (y-1))/y) - 1/y

Homework Equations

The Attempt at a Solution

 

[SansaRubic]

You do not need to use variable substitution to solve this integral. Simply set up the problem as an iterated integral. Then figure out which variable is going to be easiest to start with.