Let \(\mathrm{f}:\mathrm{R}\to \mathrm{R}\) be a function defined by \(\mathrm{f}\left(\mathrm{x}\right)=\left(2+3\mathr…

Let \(\mathrm{f}:\mathrm{R}\to \mathrm{R}\) be a function defined by \(\mathrm{f}\left(\mathrm{x}\right)=\left(2+3\mathrm{a}\right){\mathrm{x}}^{2}+\left(\frac{\mathrm{a}+2}{\mathrm{a}-1}\right)\mathrm{x}+\mathrm{b},\mathrm{a}\neq 1\). If \(\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y})+1-\frac{2}{7}\mathrm{xy},\) then the value of \(28\sum _{i=1}^{5}|f\left(i\right)|\) is:

[JEE Main 2025, 28 Jan (Shift 1)]