To what interval I must we restrict the parameter t if the graph of the parametric equations \(\begin{align*} x&=t+1,\\ y&=2t^2 +1 \end{align*}\) for \(t\in I\) is identical to the graph of the parametric equations \( \begin{align*} x&=1+\sin s,\\ y&=2-\cos(2s) \end{align*}\) for \(s\in[0,\pi)\)?
