Replace variable with value prior to evaluating NIntegrate

Question

The title says it all. Reading posts such as this however, I'm not seeing how to do this. This is the simplest example that can show my problem.

f = c/x;
a = a1;
b = b1;
NIntegrate[f, {x, a, b}] /. {a1 -> 1, b1 -> 4, c -> 2}

Answer 1

You just have to make the substitution in both the function and limits before NIntegrate. Simple example:

f = c/x;
NIntegrate[f /. #, {x, a, b} /. #] & @ {a -> 1, b -> 4, c -> 2}

Answer 2

Holding NIntegrate Unevaluted also works.

Unevaluated[NIntegrate[f, {x, a, b}]] /. {a -> 1, b -> 4, f -> 2/x}
(* 2.77259 *)

Answer 3

Maybe little odd method:

g[f, {x, a, b}] /. {a1 -> 1, b1 -> 4, c -> 2, g -> NIntegrate}