A curve called Cornu's spiral is defined by the parametric equations $$x=C(t)=\int_{0}^{\,t} {\cos(\pi u^2/2)}\,du$$ $$y=S(t)=\int_{0}^{\,t} {\sin(\pi u^2/2)}\,du$$ where $C$ and $S$ are the Fresnel functions.

Find the length of Cornu's spiral from the origin to the point with parameter value $t$ (where $t > 0$). Your answer may depend on $t$.

Length of curve =