Let for some \(\alpha \in \mathrm{R},f:\mathrm{R}\to \mathrm{R}\) be a function satisfying \(f(x+y)=f(x)+2{y}^{2}+y+\alp…

Let for some \(\alpha \in \mathrm{R},f:\mathrm{R}\to \mathrm{R}\) be a function satisfying \(f(x+y)=f(x)+2{y}^{2}+y+\alpha xy\) for all \(x,y\in R\). If \(f(0)=-1\) and \(f(1)=2\), then the value of \(\sum _{n=1}^{5}(\alpha +f\left(n\right))\) is:

[JEE Main 2026, 4 Apr (Shift 2)]