numerical integration – intetegrate problems

Sorry, I'm locked up again by Mathematica, every exit is blocked and can not find answers on the web. This usually happens when the code is long, so it is difficult to debug and show the questions. We are sorry

  1. Why can not I define a function that calls Nintegrat? It seems to want to integrate immediately with the existing values. Must sit down NIntegrate Right in my table generation, the code is very hard to read and change. Neither F[k_] or F[k:_] is working. I do not understand the difference.

  2. when I tried to swap a new one NIntegrate based on a manual integration by parts, it is more stable in single-integration than the old ones, but when they are exchanged in the table entries for it, they have {braces} and do not plot.