Laplace transform on a finite interval $f(t)= \int_0^1 e^{-xt} f(x) \, dx$

Question

What is the name of this transform? It's basically the Laplace transform where we integrate over a finite interval.

$$ F(t)= \int_0^1 e^{-xt} f(x) \, dx$$

Is it still just the Laplace transform? Sure we can make the change of variables, $y = \frac{x}{1-x}$ but is there name for the transform when written this way?