Continuous function with $\lim_{x \rightarrow + \infty}f(x)=0$ and $\lim_{x \rightarrow - \infty}f(x)=0$ is uniformly continuous
Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.