5. The curve \(y = \mathrm { f } ( x )\) passes through the point \(P ( - 1,3 )\) and is such that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 4 } { x ^ { 3 } } , \quad x \neq 0$$
- Find \(\mathrm { f } ( x )\).
- Show that the area of the finite region bounded by the curve \(y = \mathrm { f } ( x )\), the \(x\)-axis and the lines \(x = 1\) and \(x = 4\) is \(4 \frac { 1 } { 2 }\).