While we can't make a direct comparison between specific items in group A to group B, what we can do is look at individual items and think about how they can be seen as white or black box testing. In this way we can say that both integration and differentiation can be seen as both white or black box testing depending on our chose method.
Take differentiation as an example. If we don't know the function we can still differentiate over it using the "delta" method. If all we have is access to the f(x) aspect of the differentiate
, differentiation is easy by doing just (f(x+dx)-f(x))/dx. This is just like black box testing. On the other hand, we can get much more exact results, and understand the function and it's derivative. This method is like when we do f(x) = x^2 => f'(x) = 2*x. This is like white box testing.
We see similar methods can be applied to integration. Where methods like the rectangular integration method stands in for black box testing, while a more exact calculus-based approach stands in for white box testing.
Well, derivation is like white-box testing. You start with an equation and the derivation operation produces an exact equation describing the output. On the other hand, integration is like black box testing, in that the output equation always contains an unknown component. Just as with a black box, where we can test and never really determine with certainty whether the black box will perform correctly for all our possible inputs.