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?

Thanks for the update Daniel.

I don't know if this helps in isolating the problem, but here is another oddity related to the bug. f[t_] = Piecewise[{{Exp[-t], 0 <= t < 1}}] x=Range[5] Integrate[f[t] + f[t - 2], {t, -1, 4}] (* results in 2(-1+e)/e ) Integrate[DiracDelta[t] + f[t] + f[t - 2], {t, -1, 4}] ( results in (-1+e)/e ) Integrate[Sum[x[[k]] f[t - 2 k], {k, 1, 5}], {t, -1, 20}] ( results in 15(-1+e)/e ) Integrate[DiracDelta[t] +Sum[x[[k]] f[t - 2 k], {k, 1, 5}], {t, -1, 20}] ( results in (-1+e)/e *) I tried the weighted sum of functions since in the notebook that I first encountered the problem, adding the delta function to the weighted sum resulted in not even being able to calculate the integral. In the example above Mathematica computed the integral; it just got the wrong result.

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.

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