Disclaimer: I don't know much computational complexity theory. I am nevertheless curious.
If function $f(x)$ has a certain level of computational complexity (which I actually don't know how to measure), what can we then say about the computational complexity of the following indefinite integral?
$$\int f(x) \, \mathrm d x$$
For example, can we say something about how long it takes to approximate the integral of $f$ within an error of $\epsilon$, given that we know how long it takes to compute $f$ within an error of $\epsilon$?