5 In this question, \(I\) denotes the definite integral \(\int _ { 2 } ^ { 5 } \frac { 5 - x } { 2 + \sqrt { x - 1 } } \mathrm {~d} x\). The value of \(I\) is to be found using two different methods.
- Show that the substitution \(u = \sqrt { x - 1 }\) transforms \(I\) to \(\int _ { 1 } ^ { 2 } \left( 4 u - 2 u ^ { 2 } \right) \mathrm { d } u\) and hence find the exact value of \(I\).
- (a) Simplify \(( 2 + \sqrt { x - 1 } ) ( 2 - \sqrt { x - 1 } )\).
(b) By first multiplying the numerator and denominator of \(\frac { 5 - x } { 2 + \sqrt { x - 1 } }\) by \(2 - \sqrt { x - 1 }\), find the exact value of \(I\).