Area integral question.?

Question

I=int((r^2)+1)dA

What is the value of this for a square of side length 2 centred at the origin with sides parallel to the x and y axes?

Answer 1

1st : 8 * int over [0,π / 4] for Θ and [ 0, sec Θ] for r of { (r² + 1) r dr dΘ}

2nd:  int over [0,2π] for Θ and over [ 0,2] for r of the same functions above