Here $1<p<\infty$, prove that $G=\{f\in L\_p(\mu): \int\_\mathbb{R} f(t) dt = 0\}$ is a dense subset of $L\_p(\mu)$, where $\mu$ is the Lebesgue measure on $\mathbb{R}$.

How to prive this? I have no idea, can anyone give me a hint?