The Oscillation of a Function

For a function $f$ on $[a, b]$, define its oscillation $d(a, b)$ as the difference between its maximum and minimum there.

1. If $f(x) = x^2 - 2x + 2$, find $d(1, 2)$. 2. If $f(x) = x + \dfrac{m}{x}$ and $d(1, 2) \ne |f(2) - f(1)|$, find the range of $m$.