5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8f97853c-812f-4b7b-9d40-2de7a85886c0-12_832_931_260_502}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The straight line \(l\) with equation \(y = \frac { 1 } { 2 } x + 1\) cuts the curve \(C\), with equation \(y = x ^ { 2 } - 4 x + 3\), at the points \(P\) and \(Q\), as shown in Figure 2
The finite region \(R\) is shown shaded in Figure 2. This region \(R\) is bounded by the line segment \(P Q\), the line segment \(T S\), and the arcs \(P T\) and \(S Q\) of the curve.
Use integration to find the exact area of the shaded region \(R\).