Comment #1 on issue 3801 by [email protected]: Piecewise integration failure
http://code.google.com/p/sympy/issues/detail?id=3801
You could try make your left and right boundaries have opposite signs:
var('n',negative=True)
n
var('p T',positive=True)
(p, T)
f=Piecewise((0,t<n),(x,t>=n),(0,t>=p))
integrate(f,(t,n,T))
-n*x + x*Min(T, p)
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