Plot The Cornu Parametric Spiral

How do I plot the Cornu parametric spiral in 3D with Mathematica. The 2D is quite easy. For more details, you need to be familiar with the Cornu statement.

$$\begin{cases} x(t)=\int_{0}^{t}\cos(u^{2})du&\\ y(t)=\int_{0}^{t}\sin(u^{2})du& \end{cases}$$

body[t_] = Integrate[#[u^2], {u, 0, t}] & /@ {Cos, Sin}

ParametricPlot3D[body[t]~Join~{t}, {t, -2 Pi, 2 Pi},