I'm confused about the notation used, pretty much everywhere, to describe what a Laplace transform it.
Wikipedia says something along the lines of "..Laplace transform of a function $f(t)$..", mathworld similarly has this definition
$\mathcal L_t[f(t)]=\int_0^\infty f(t)e^{-st}dt$
What's strange to me is that $f(t)$ here is treated as a function instead of a number ($f$ is the actual function here).
This isn't unusual in mathematical texts and perhaps only a little bit annoying sometimes but I feel like in this case there's some special significance.
What's the explanation for this 'wrong' notation?