Finding moment generating function of this r.v. with double exponential dist

Question

So in the above question, we can say the moment generating function is $$m_x(t) = \frac{1}{2}\theta\int_{-\infty}^\infty e^{tx-\theta |x|} dx$$

Now, as the hint suggests, we can split the integral into two parts, $\int_0^\infty$ and $\int^0_{-\infty}$, but I can't figure out to integrate that function. Any help? Thanks!