Let $f$ be a polynomial function, $$ f(x) = a_0 + a_1 x + ... + a_d x^d $$ where $a_0$, $a_1$, ..., $a_d$ are parameters and usually $d \le 6$.
Let $g$ be the line integral of $f$, $$ g(x) = \int_0^x \sqrt{1 + f'(x)^2}dx $$
Now I want to know $g^{-1}(y)$, where $y$ = $1, 2, ..., m$.
Do you have any suggestions on how I should calculate it?
Notice: The answer is not necessary close-formed, it is ok as long as fast and accurate.