fluid dynamics - Integrating pressure over a surface

Consider the 2D airfoil below.

_{(source: gsu.edu)}

In engineering (and maybe physics) you will often see something like the following as an expression for the pressure force acting on a surface (in this case a curve but imagine it having unit depth into the screen).

$$ \mathrm{d} \mathbf{F} = p \, \mathrm{d} \mathbf{s} \\ \text{where} \, \mathrm{d} \mathbf{s} = \mathbf{\hat{n}} \, \mathrm{d} s $$

If you attempt to integrate this over a curve C to find the force you get;

$$ \int_?^? \mathrm{d} \mathbf{F} = \int_C p \, \mathrm{d} \mathbf{s} $$

where there doesn't seem to be obvious corresponding limits for integrating on the LHS. Is it fine to consider the limits as from 0 to $\mathbf{F}$ or is this some kind of engineering "shorthand" that you often see which makes no sense mathematically. I am trying to interpret it as a "change in force" but it doesn't really make sense to me.