Existence of bounded continuous $f:\mathbb{R} \to \mathbb{R}$ st. $\sup_{n \in \mathbb{N}}| \int_{-n}^{n} f(t)\sin(2 \pi n t)dt| = \infty$

Question

Existence of $f:\mathbb{R} \to \mathbb{R}$ st. $\displaystyle \sup_{n \in \mathbb{N}} \big| \int_{-n}^{n} f(t)\sin(2 \pi n t)dt \big| = \infty$

I already proved that the space of continuous limited functions $C_b (\mathbb{R})$ is a Banach space with $\| f\| = \sup|f|$. But I don't know how to proceed to find this function.

Any help would be appreciated.

Thanks.