6 It is given that, for non-negative integers \(n\),
$$I _ { n } = \int _ { 0 } ^ { \pi } x ^ { n } \sin x \mathrm {~d} x$$
- Prove that, for \(n \geqslant 2 , I _ { n } = \pi ^ { n } - n ( n - 1 ) I _ { n - 2 }\).
- Find \(I _ { 5 }\) in terms of \(\pi\).