Suppose that $f\left(x\right)\geq0$ is continuous on $\left[-\infty,\infty\right]$ and $\int_{-\infty}^{\infty}f\left(x\right)dx=1$. Is it true that $\int_{-\infty}^{\infty}\left|x\right|f\left(x\right)dx\leq\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\left|x-y\right|f\left(x\right)f\left(y\right)dxdy$?

Thanks.