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You can also use the integral from 0 to b minus a, integral from 0 to b minus a dxdy. ...

No one is arguing – it's just a specific case of what I wrote.

I think the whole point is that the sides of the square are not parallel to the OX and OY axes.

Actually, the question from Rapper doesn't ask how to find the area of a figure bounded by lines with given equations. The question is how to find the area of a square using a multiple integral, so nothing prevents us from setting the coordinate axes parallel to its sides, and we can even place one of the vertices at the origin so that the figure is in the first quadrant, then the integrals will be from zero.
And even in the case of sides that are not parallel to the coordinate axes, an orthogonal transformation of the coordinate system (rotation) does not change the differential of the area, and with its help, the axes can be made parallel to the sides.