Updates:
        Status: Accepted
        Labels: Integration Polynomial

Comment #1 on issue 2128 by asmeurer: cannot integrate piecewise function numerically
http://code.google.com/p/sympy/issues/detail?id=2128

In master, Integral(f, (x, -oo, oo)).evalf() hangs, Integral(f, (x, -oo, oo)).doit() gives "DomainError: there is no field associated with RR". Since the latter is a polys error, I tried it in Mateusz's polys11 branch, and got

In [3]: integrate(f, (x, -oo, oo))
Out[3]: 1.08063375955856

So the issue will be fixed whenever polys11 gets merged in (assuming that is the correct answer there).

By the way, I did notice that your expressions shows some printing problems with Piecewise. The "+" for the innermost nested piecewise functions should be centered, as should the "dx". In all, it's hard to read anyway (though applying piecewise_fold() a few times makes it a little better).

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