Mathematics Question from JEE Main 2025 · 28 January, Shift 1

Let $f: \mathbb{R} \to \mathbb{R}$ be a function defined by $f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1$. If

$$f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy,$$

then the value of $28 \sum_{i=1}^5 \left| f(i) \right|$ is: