measure theory - Prove that $lim_{n to infty} int_{-infty}^{infty} sin(nt) f(t) d t = 0$.

I am trying to prove that $\lim_{n \to \infty} \int_{-\infty}^{\infty} \sin(nt) f(t) d t = 0$ for every Lebesgue integrable function $f$ on $\mathbb{R}$. My first thoughts were to use Dominated Convergence Theorem but I realised that there is no pointwise limit of the sequence of functions $f_n = \sin(nt) f(t)$. I do not know how to proceed.

Any help would be appreciated. Thanks!