The curve \(C\) has parametric equations
\(x=t^{2}, \quad y=t-\frac{1}{3} t^{3}, \quad \text { for } 0 \leqslant t \leqslant 1 .\)

Find
(i) the arc length of \(C\),

(ii) the surface area generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.