2024 DHS P1 Q1

For \(a>4\), show that \(\displaystyle\displaystyle \displaystyle\int_{0}^{a}{\left| 2{{x}^{2}}-3x-2 \right|\,\,\mathrm{d}x}=\frac{1}{k}\left( 4{{a}^{3}}-9{{a}^{2}}-12a+56 \right)\) where \(k\) is an integer to be found.[4]