There is a package called pw.mac for Maxima from https://sourceforge.net/projects/piecewisefunc/ This package has a pwdelta() function that behaves as you expect.
pwint() means integrate,
pwint(pwdelta(x-a)*x^2,x,minf,inf);
a^2;
The package is for piecewise functions. See the help for more information.
FWIW,
Rich
> load(delta)&
> delint(delta(x),x,-1,1);
>
> which returned 3. In fact, it returned three for every set of limits
> I tried, whether minf,inf or 0,0 or anything else.
>