Is integration/differentiation an inverse relation? A:
$\frac{d}{dx}(\sin(x)) = \cos(x)$,
$\int(\cos(x)) = \sin(x) + C$
B:
$\sin(\arcsin(x)) = x$
Both A and B are inverse relations?  A goes full circle with a FUNCTION, and B goes full circle with a VARIABLE.  
Despite this, are they the same notion of "inversion"?   
**Addition: is A inverse by composition while B inverse simply by the definition of inverse?

You can think of integration (with constant term $0$) and differentiation as functions that have real valued functions as inputs and outputs. Then these functions are inverses of each other, just like $\sin$ and $\arcsin$.
