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\includegraphics[max width=\textwidth, alt={}, center]{be0fb208-2ef1-4fae-84ff-ad2e8bf2dcc5-16_446_956_260_593} The diagram shows the curve \(y = \left( 1 + x ^ { 2 } \right) \mathrm { e } ^ { - \frac { 1 } { 2 } x }\) for \(x \geqslant 0\). The shaded region \(R\) is enclosed by the curve, the \(x\)-axis and the lines \(x = 0\) and \(x = 2\).

1. Find the exact values of the \(x\)-coordinates of the stationary points of the curve.
2. Show that the exact value of the area of \(R\) is \(18 - \frac { 42 } { \mathrm { e } }\).