7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e3faf018-37a8-48ef-b100-81402a8ec87f-09_696_821_205_516}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The curve \(C\) has equation \(y = x ^ { 2 } - 5 x + 4\). It cuts the \(x\)-axis at the points \(L\) and \(M\) as shown in Figure 2.
- Find the coordinates of the point \(L\) and the point \(M\).
- Show that the point \(N ( 5,4 )\) lies on \(C\).
- Find \(\int \left( x ^ { 2 } - 5 x + 4 \right) \mathrm { d } x\).
The finite region \(R\) is bounded by \(L N , L M\) and the curve \(C\) as shown in Figure 2.
- Use your answer to part (c) to find the exact value of the area of \(R\).
\section*{LU}