Integration is often said to be a global operation. I suppose that this refers to the fact that the integral $$ \int_{a}^{b} f(x) \, dx $$ depends on the value of $f(x)$ on an entire interval $[a,b]$. This is in contrast to the derivative, which simply depends on behaviour of a function around a given point.
However, in practice to compute the above integral I would simply find an antiderivative of $f$ and apply the fundamental theorem of calculus. And since antidifferentiation seems as local as differentiation, I don't understand how this explains why the mechanical process of integration (both indefinite and definite) is so much harder than differentiation.
For a reference, Terry Tao makes this statement in the following Math Overflow post: 'Why is differentiation mechanics and integration art?'.
