Updates:
        Status: NeedsDecision

Comment #1 on issue 3732 by asmeu...@gmail.com: Integration of Piecewise function should also be continuous
http://code.google.com/p/sympy/issues/detail?id=3732

This requires some thought. What is the reason that you would prefer it to be this way?

I can think of at least one reason not to do it, which is that if the expression is complex (i.e., lots of symbolic constants independent of x), then the terms that it will add to each section of the Piecewise will be large and make it much more complex than it otherwise would be.

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