Show $\int _ 0 ^\infty \frac {\sin ( x^2 + ax )}{ x } dx$ converges for $a\ge 0$

Question

I want to show that $f(a) = \int _ 0 ^\infty \frac {\sin ( x^2 + ax )}{ x } dx$ converges for all $a \ge 0$ and $f$ is continuous on $[0, \infty ) $.