2 In this question, you must show detailed reasoning.
A curve is defined parametrically by \(x = t ^ { 3 } - 3 t + 1 , y = 3 t ^ { 2 } - 1\), for \(0 \leqslant t \leqslant 5\). Find, in exact form,

1. the length of the curve,
2. the area of the surface generated when the curve is rotated completely about the \(x\)-axis.