Representation of power series of product of sine and cosine Given $$ f(x)= \int \limits_0^x \sin(y^2) \cos(y^2) \mathrm{d}y $$
Anyone can help and guide me for this?I don't really have an idea of how to represent it as power series
Thank you!
My attempt: $$ 0.5\int_{0}^x \sum_{n=0}^\infty \frac{{(-1)}^n{({2{y}^{2})}}^{2n+1}}{(2n+1)!} \mathrm{d}y$$ after substituting Maclaurin series of sin x

Hint:
$$\int_0^x\sin t^2\cos t^2\;dt=\frac12\int_0^x\sin 2t^2\;dt$$
and then you may want to check Fresnel Integrals
