Hi Dent,

Thank you for your answer. I went through it. What I ment with "adding the constants manually" was actually resembling your approach; using the functions defined in the attached notebook, I recreated the "manual steps", being:

HyWithFirstConstant[x_, y_] = HyNoConst[x, y] - Piecewise[{{HyNoConst[x, -1], -1 <= y <= 1}}];
HyWithAllConstant[x_, y_] = HyWithFirstConstant[x, y] + Piecewise[{{HyWithFirstConstant[x, 1], 1 < y}}];

Sorry for being unclear about what I ment with the manual step. And indeed this is doable (but I would not say "without labor", the number of piecewise parts might be way higher). What I've learned from your answer are two things:

1. The use of PiecewiseExtend, which produces a flattened-condition form of the function that shows the "conditional-areas" in the function clearly; including condition-border mistakes I made.
2. The use of "If" i.s.o. "Piecewise", which is shorter and seems less error prone regarding condition-borders.

I do get your point in that it is not easy in general to find the intended integration constantants in 2D (or nD). However I do not see if the integration is simply along the y-axis, how this can lead to non-axis parallel constants.

I still feel that the (rather mechanical an repetitive procedure when there are a lot of piecewice parts of the) manual steps that we seem to have do should be performed automatically by Mathematica. If the function would be to complex/irregular for Mathematica to do it automatically a certain feed back to the user should indicate it then (instead of not finding constants for simple cases). I'm curious if other symbolic solvers like Maple can derive the constants for 2D integrals in an automatic way.

Thanks again for your answer, Koen