I have observed what seems to be a bug when attempting to integrate an expression that is the sum of a Dirac Delta function and a continuous function (with discontinuities at the end-points). I attempted to find if this is discussed in the documentation, but did not see anything. A very simple example is shown below. g[t_] = Piecewise[{{Exp[-t], 0 <= t < 1}}] Integrate[DiracDelta[t] + g[t], {t, -1, 2}] (* results in (e-1)/e *) but Integrate[DiracDelta[t], {t, -1, 2}] integrates correctly I did notice that if the function is not defined as a piecewise function the correct answer is obtained In[320]:= Integrate[DiracDelta[t] + Exp[-t], {t, 0, 1}] Out[320]= 1 - 1/E + HeavisideTheta[0] Am I using Mathematica incorrectly or is this a bug. Is there any workaround other than pulling the delta function out of the integral and accommodating it separately?

The issue was not what I expected but rather a typo that resulted in part of the integral being discarded. Will be fixed (along with the newer examples). I apologize for any inconvenience this may have caused.

A bug. Explicitly splitting the sum will show this. g[t_] = Piecewise[{{Exp[-t], 0 <= t < 1}}]; Integrate[DiracDelta[t] + g[t], {t, -1, 2}] (* Out[278]= (-1 + E)/E ) Integrate[DiracDelta[t], {t, -1, 2}] + Integrate[g[t], {t, -1, 2}] ( Out[279]= 1 + (-1 + E)/E *) My guess, which at some point I will try to check, is that the integration range gets split due to the `Piecewise`, and the fact that the delta has its payload at a boundary point causes trouble.

Thanks for confirming that it is a bug Daniel. If that is not a known bug, can you report it to whomever should be told about it or should I submit a bug report?

Integrate sum of dirac delta and a piecewise defined continuous function?