Laplace transform double function

Question

I'm trying to find the Laplace transform of the function $$f(t) = \begin{cases} 1, & 0\le t < \pi\\ 0, & \pi\le t< \infty \end{cases}$$

Answer 1

Rewrite $f(t)$ as follows:

$$f(t)=u(t)-u(t-\pi)\tag{1}$$ Now use $$\mathcal{L}[u(t)]=\frac{1}{s}$$ and $$\mathcal{L}[g(t-a)]=e^{-as}\mathcal{L}[g(t)]$$ and the linearity of the Laplace transform to find the laplace transform of $(1)$.