4 It is given that, for \(n \geqslant 0\),
$$I _ { n } = \int _ { 0 } ^ { 1 } x ^ { n } e ^ { - x ^ { 2 } } d x$$
- Find \(I _ { 1 }\) in terms of c .
- Show that
$$I _ { n + 2 } = \frac { n + 1 } { 2 } I _ { n } - \frac { 1 } { 2 \mathrm { e } }$$
- Find \(I _ { 5 }\) in terms of \(e\).