Given a differentiable function y=f(x) on [a,b], and a regular partition

a=x0<x1<...<xn-1<xn=b

explain how approximating the arc segment length deltaLi by a straight line, then letting n -> infinity, leads to a definite integral for the total length

L = integral from a to b sqrt(1 + (f'(x))^2) dx

i was given this question just after being taught integration by parts ... and i cannot understand anything about it ... if someone could provide me with details on how to solve it ... not just the solution ... that would be great as this is due tomorrow