How to declare undefined mathematical function

[marktbaldridge]

I would like to declare a function say, x(t) but without saying what x(t) is.

Thus when I evaluate an integral from -infinity to infinity of dirac(τ)x(t-τ) dτ

the answer should be x(t). Now, this would work with sin(x) because there is no simplification of sin(x).

Is there a way to define such a function? And how would the syntax work to make sure x(t-tau) is functional notation, not x*(t-τ).

Thank you!

(See attachment for the integral I'm trying to evaluate.)