The Fresnal S integral can be represented with the following:
$$F(a,b)=\int_a^b{\sin(x^2)}\,dx = \frac{-\sqrt{i\pi}}{4}[\operatorname{erfi}(\sqrt{i}\,b)-\operatorname{erf}(\sqrt{i}\,b)]+\frac{\sqrt{i\pi}}{4}[\operatorname{erfi}(\sqrt{i}\,a)-\operatorname{erf}(\sqrt{i}\,a)]$$
Using the complex definition of sine and two u-subs. What kinds of applications could this property of the Fresnal S integral be used for in real life applications?