Laplace Transform of Integral

Theorem
Let $f: \R \to \R$ or $\R \to \C$ be a function.

Let $\laptrans f = F$ denote the Laplace transform of $f$.

Then:
 * $\displaystyle \laptrans {\int_0^1 \map f u \rd u} = \dfrac {\map F s} s$

wherever $\laptrans f$ exists.