I have been working on this for several days but getting nowhere. Any help would be great.

\begin{align}

&\int_0^x dy\,y^2 \cos(y^2) C^2 \!\!\left(\!\frac{\sqrt{2}\,y}{\sqrt\pi}\!\right)

\end{align}

In reality only the first one is causing me troubles, however I have pasted the entire expression as it might lead to some cancellations. Any help would be welcome. $C()$ is the Fresnel integral.