Expected value of a continuous random variable

Assume that the probability density function $f(x)$ of the random variable $X$ is symmetric with respect to $a$, i.e.

$$f(a + x) = f(a - x).$$What is the expected value of $X$?

Tip: Draw a graph of a symmetric function. Why $\int\limits_{-\infty}^{+\infty}xf(x)dx=0$ if $f(x)$ is symmetric with respect to $0$?