I need to evaluate the Laplace transform of the following integral:
$$ \phi(t)= \int_0^{t_0} K(t-x)f(x)dx $$
Note that the constant upper limit of the integral is different from the time variable, so that straightforward application of the Convolution Theorem is not feasible. I have an explicit functional form of the Laplace Transform of the Kernel $K()$, but not of the function $f()$ or its transform.
Any tips, pointers, hints or even answers would be deeply appreciated.
Thanks