# How does Wolfram Language deal with DiracDelta[0] in Integrate command?

GROUPS:
 Hi, I'm trying to compute the following integral involving derivatives of Heaviside step function, which on integration by parts gives DiracDelta[0] which is undefined or infinite. Integrate[f[x]D[D[HeavisideTheta[x],x],x],{x,0,2}] But Mathematica seems to be making the term containing DiracDelta[0] as zero. I have attached the Mathematica file for a clear understanding of my query. Any help is much appreciated. Attachments:
 Daniel Lichtblau 1 Vote Integrate across the origin e.g. from -2 to 2. Integrate[f[x] D[D[HeavisideTheta[x], x], x], {x, -2, 2}] (* Out[5]= -Derivative[1][f][0] *) Integrating that particular expression with 0 as an endpoint of the integration interval is in effect GIGO ("garbage in, garbage out").