Polynomial functions

Q. Let $a,b,cϵR$. If $f\left(x\right)=a{x}^2+bx+c$ be such that $a+b+c=3$ and $f(x+y)=f\left(x\right)+f\left(y\right)+xy,\forall x,yϵR,\text{then}{\sum }_{n=1}^{10}f\left(n\right)$ is equal to

1. 330
2. 165
3. 190
4. 255