[JadeNB]

> Likewise, it's often valuable to define integration as nothing more than the relationship such that

    >  I(region, derivative(quantity)) 
    > = I(boundary(region), quantity)

> which is known as the Generalized Stokes Rule.

I like your explanation very much, but I think that calling the integral 'the relationship' (emphasis on the definite article) satisfying Stokes is an overstatement. There are many such; for example, I(_, _) = 0.

[tel]

Generally my whole argument is heavy on existence and light on uniqueness, but it's a great point to emphasize it! :)