Solving Problem Integral Figure: -256/5 or -96/5?

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Figure for example

1. ∫∫dydx
2. ∫∫x dydx

(x²<= y <= 4) and (-2 <= x <= 2)

1. Two method get the same answer
2. Two method get the different answer
- between answers 0 or 8 , the correct answer is ?

I met this problem with my problem

∫ (x^4 + y^2)dx +(2x^2-y^4)dy = ∫∫ [(4x - ( 2y )] dA

∫∫ [(4x - ( 2y )] dA
∫∫ [(4x - ( 2y )] dydx (x²<= y <= 4) and (-2 <= x <= 2)
∫ [ 4xy - y² ] dx (x²<= y <= 4) and (-2 <= x <= 2)

and

between -256/5 or - 96/5 the correct answer is

 

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