Consider a rational function $f(x)= \dfrac {x^{2} - 3x - 4}{x^{2} - 3x + 4}$ and a quadratic function $g(x) = x^{2} - (b + 1) x + b - 1$, where $b$ is a parameter. The sum of integers in the range of $f(x)$, is

The function f(x) = (x^2 - 3x - 4) / (x^2 - 3x + 4) can be rewritten as 1 - 8 / (x^2 - 3x + 4). The quadratic x^2 - 3x + 4 has a minimum value of 7/4 at x = 1.5, so the expression 8 / (x^2 - 3x + 4) ranges from 8/(infinity) to 8/(7/4) = 32/7. Thus, f(x) ranges from 1 - 32/7 = -25/7 to 1 - 0 = 1. The integers in this range [-3.57, 1] are -3, -2, -1, 0, 1. Their sum is -5.