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Maxima doesn't know how to integrate the Dirac function, so neither does Sage. From their docs:

Currently only laplace knows about the delta function.

Sage actually even mentions this use case in the manual.

But after all, it's not a function. You can integrate against it is all, but there is no symbolic integral, I guess.

I think that something similar is true for the Heaviside function.

That doesn't mean it couldn't be implemented, but there are no tickets open for this.