Hint: by definition

\(\displaystyle{L}{\left({f}\right)}{\left({s}\right)}\:={\int_{{0}}^{{\infty}}}{f{{\left({t}\right)}}}{e}^{{-{s}{t}}}{\left.{d}{t}\right.}={\int_{{0}}^{{\pi}}}{0}\cdot{e}^{{-{s}{t}}}{\left.{d}{t}\right.}+{\int_{{\pi}}^{{\infty}}}{\sin{{t}}}{e}^{{-{s}{t}}}{\left.{d}{t}\right.}={\int_{{\pi}}^{{\infty}}}{\sin{{t}}}{e}^{{-{s}{t}}}{\left.{d}{t}\right.}\)

Using \(L(f)(s) := \int_0^{\infty} f(t)e^{-st} dt=\int_0^{\pi} 0 \cdot e^{-st} dt+\int_{\pi}^{\infty} \sin te^{-st}dt=\int_{\pi}^{\infty}\sin te^{-st} dt\) you can arrive at the answer.