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Integrate UnitStep, Bug?


The following code returns the incorrect result (-a+b) UnitStep[a-b]. It
should be Min[a,b].

fr[e_]=UnitStep[-e];
fl[e_]=UnitStep[-(e-b)];
Integrate[fl[e](fr[e-a]-fr[e]),{e,-Infinity,Infinity},Assumptions->{b>0,a>0}]

Is this a known bug? Should I avoid using step functions with Integrate?
Any comments appreciated.


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