Suppose you want to evaluate the line integral \begin{equation} W = \Lint \FF\cdot d\rr \end{equation} and you have an explicit parameterization $\rr=\rr(u)$ of the curve. You can differentiate this expression in order to determine \begin{equation} d\rr = {d\rr\over du}\,du \label{drparam} \end{equation} thus turning your line integral into an ordinary integral with respect to $u$.

This is essentially the strategy used in most calculus texts: the distance you go is $ds=|d\rr|$, the direction you are going is given by the unit tangent vector $\TT$, the component of $\FF$ in your direction is $\FF\cdot\TT$, and so the work done when moving a small distance is $\FF\cdot\TT\,ds$. But \begin{equation} \TT \, ds = {d\rr\over ds} \, ds = d\rr \end{equation} so you wind up with the same integral as before. This is nice in theory, but in practice it is not always easy to express physical quantities explicitly in terms of the arclength $s$; it's usually easier to work with some other parameterization, which brings us back to ($\ref{drparam}$). A common special case for line integrals that involve actual motion along the curve, such as work, is to use time $t$ as the parameter, in which case $d\rr=\vv\,dt$, where $\vv$ is the velocity.