Optimal antiderivative \[ \frac {\cos \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{b \pi }+x \,\mathrm {S}\left (b x \right ) \]
command
integrate(fresnel_sin(b*x),x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \frac {b x \operatorname {S}\left (b x\right ) + \frac {\cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{\pi }}{b} \]
Maxima 5.44 via sagemath 9.3 output
\[ \int {\rm fresnels}\left (b x\right )\,{d x} \]________________________________________________________________________________________