\[ \int S(b x) \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \]
Optimal antiderivative \[ \frac {\mathrm {S}\left (b x \right )^{2}}{2 b} \]
command
integrate(fresnel_sin(b*x)*sin(1/2*b^2*pi*x^2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\operatorname {S}\left (b x\right )^{2}}{2 \, b} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left ({\rm fresnels}\left (b x\right ) \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ), x\right ) \]