On Wikipedia's article on Laplace transform the following property is listed: $$\mathcal{L}\left\{f(t)/t\right\} = \int_s^\infty F(\sigma)d\sigma. $$ A question about this property has been asked before but does not address my concerns.
Since $s$ is complex, the integral and in particular its limits don't make too much sense. Is the idea to treat $s$ and $\sigma$ as real parameters, and then extend to $s$ complex by analytic continuation?