Comment #67 on issue 1695 by smi...@gmail.com: integral of a piecewise function gives bad result
http://code.google.com/p/sympy/issues/detail?id=1695

At https://github.com/smichr/sympy/tree/1695 there is a start to this that gives:

    h[2] >>> integrate(Piecewise((3,x<2),(exp(x),x<5),(x,True)),(x, 0, x))
Piecewise((3*x, x < 2), (6 - exp(2) + exp(x), x < 5), (-13/2 + x**2/2 - exp(2) +
     exp(5), True))
    h[3] >>> integrate(Piecewise((3,x<2),(exp(x),x<5),(x,True)),(x, x, 0))
Piecewise((-3*x, x < 2), (6 + exp(2) - exp(x), x < 5), (13/2 - exp(2) - x**2/2 +
     exp(5), True))



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