Standard normal random variable and their sum

Question

Suppose $X_1$ is a standard normal random variable. Define $X_2$ as $X_2$ $=$ $-X_1$ if $|X_1|<1$ , and $X_2$$=$$X_1$ , otherwise.

(a) Show that $X_2$ is also a standard normal random variable. (b) Obtain the cumulative distribution function of $X_1 + X_2$ in terms of the cumulative distribution function of a standard normal random variable.