# How do you find the length of a curve using integration?

If you want to find the arc length of the graph of $y = f \left(x\right)$ from $x = a$ to $x = b$, then it can be found by
$L = {\int}_{a}^{b} \sqrt{1 + {\left[f ' \left(x\right)\right]}^{2}} \mathrm{dx}$