First, there is no need to call integrate each time for different f. Evaluate the integral outside the Table and it be a function of f, then simply evaluate for different f. Much faster. Only case to worry about is zero value, for this need to take the limit. But this is much faster than calling Integrate each time. For the plot, simply use Table with {x,y} in it, like this

int = Integrate[Exp[-a (2 \[Pi] f \[Eta] L)/U ] L  , {\[Eta], 0, 1}]; (*integrate once*)
g[x_] := If[x == 0, Limit[int, f -> 0], int /. f -> x];
data = Table[{i, g[i]}, {i, 0, 4000}];
ListLinePlot[data]

ps. you use UpperCaseLetter for your variables. Not a good idea since these are reserved for Mathematica and can cause problem sometimes. Better to use lowerCaseLetter