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\includegraphics[max width=\textwidth, alt={}, center]{2ae05b46-6c9f-4aaa-9cba-1116c0ec27d4-3_579_557_858_794}
The diagram shows part of the curve \(y = x ^ { 2 } - 3 x\) and the line \(x = 5\).
- Explain why \(\int _ { 0 } ^ { 5 } \left( x ^ { 2 } - 3 x \right) \mathrm { d } x\) does not give the total area of the regions shaded in the diagram.
- Use integration to find the exact total area of the shaded regions.