Fresnel sine integral

For functions involving angles (trigonometric functions, inverse trigonometric functions, etc.) we follow the convention that all angles are measured in radians. Thus, for instance, the angle of $90\,^\circ$ is measured as $\pi/2$.
The Fresnel sine integral, which we here denote by $S$, is defined as:
$S(x) := \int_0^x \sin(t^2) \, dt$