I tried considering the integral:
$$\mathcal{L}[{f(t)}](s) = \int_{0}^{\infty}e^{-st}\frac{\sin(t)}{t^2}\,dt,$$
but the function $f(t) = \dfrac{\sin(t)}{t^2}$ has a vertical asymptote at $t_0 = 0$, therefore this integral isn't defined... does this make sense?