Q:

Interactive variation of integration limit

I want to compute this function for different values of Kappa, so that I don't have to change Kappa manually. Some kind of Manipulate expression.
Integralfunc[t_] :=  
  NIntegrate[a^-2(Exp[-1/a^2]*BesselI[0, 1/a^2], {a, 0. 02, Kappa*t}]
SetAttributes[Integralfunc, Listable]
DeFunc = IntegralFunc[Range[0.1, 250, 1.25]]
ListPlot[DeFunc, PlotStyle Red]

A:

ClearAll[Integralfunc, DeFunc]

Functions that directly or indirectly use numeric techniques should have their arguments restricted to numeric values.
IntegralFunc[t_?NumericQ, Kappa_?NumericQ] :=

  NIntegrate[a^-2 (E^(-1/a^2))*BesselI[0, 1/a^2],
   {a, 0.02, Kappa*t}];

DeFunc[Kappa_?NumericQ] :=
 IntegralFunc[#, Kappa] & /@ Range[0.1, 250, 1.25]

Use a fixed PlotRange to make it easier to see the effect of changing Kappa
Manipulate[
 ListPlot[DeFunc[Kappa],
  PlotStyle -> Red,
  PlotRange -> {2.3, 2.37}],
 {{Kappa, 5}, 1, 10, .01, Appearance -> "Labeled"}]

