I know the heading may be a bit misleading one. But I can't find a better one. Anyone can suggest a good one.
By writing Weird function I mean those functions that are integrable but not easy to do so. I have come to know that uniform convergence of a series of integrable functions on some set confirms the fact that we can interchange the order of sum and integral. In other words, this leads to perform term by term integration for infinite series of functions. I am very curious about: Can we write any weird function as the limiting function of uniformly convergent series of simple integrable functions? If the answer is yes, then I think we can integrate those functions easily. But then after integrating we again have a series, that must be again uniformly convergent I think. In that case it may not be possible to write it as closed form. Is my observation is correct?