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.
 A: You are summing "small amounts of force" over "all points on the surface".
This is the tricky thing about integrals - they are not always nice one dimensional constructs with limits in the units of the quantity shown as $dx$.
The integral symbol is actually a very stylized letter S: once you realize that, you see that you are "summing something" and the limits just describe the region over which the summing happens.
In your example, the "region" is the surface of the air foil; and you cannot give "neat" numerical limits unless you find a way to parameterize the location on the foil so that you get a separation of variables. But for the concept of integration, that doesn't matter...
Note on separation of variables: if you have a rectangle parallel to X and Y, you can describe each part of the surface with x, y coordinates and area as dx dydx dy. Then the limits become $$\int_{x_1}^{x_2}\int_{y_1}^{y_2}\vec{F}(x,y)\cdot \vec n ~dx ~dy$$
I don't know if that made things clearer, or just confused you more. Comments...
A: Limits can be fuselage to the tip of the wings :) !! As some user mentioned its just a force in total, nothing to worry on the limits over the integration. If one take it as a line just summing all lines will give the area and of course the force. For example if xxxx Newtons force in a single line and summing it over the sampled area (each sample is considered as thick line) will give the total force. As sampling rate increases(sampling thickness --->0) error will come down. Integration eliminate this complexity but it depends the governing equation. 
Am I making it more complex :(
