Am I right in thinking that line integrals of the form int_c f(x,y)dx arise by approximating the arc length delta s by the line segment delta x so that as delta x tends to 0 delta s / delta x = 1?

I can undertsand int_c f(x,y)ds as dividing the curve into smaller and smaller arcs.

Is this similar to resolving vecors into i components and j components (for int_c f(x,y)dy) . The problem is that I have a poorish mechanics and phyisics backround and find some examples difficult. Thanks for any help.