Odafelé vagy visszafelé nem érvényes az integrálszámítás első tétele?

https://en.wikipedia.org/wiki/Integral#First_theorem

 

 

 

 

https://en.wikipedia.org/wiki/Inverse_function_theorem

"In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point. The theorem also gives a formula for the derivative of the inverse function. ... There are also versions of the inverse function theorem for complex holomorphic functions, for differentiable maps between manifolds, for differentiable functions between Banach spaces, and so forth."