First, we must have Clojuratica and Mathematica talking to each other. Either complete the Setting up Mathematica to dalk to Clojuratica for Mac OS X and Linux recipe or the Setting up Mathematica to talk to Clojuratica for Windows recipe. Also, we'll need to have called the init-mma function.

Also, we need to make sure that the Clojuratica namespace is imported into our script or REPL:

(use 'clojuratica)

Moreover, we need a Mathematica file to run. I created one called line-integral.m, and it contains these lines:

SyntaxInformation[
   lineIntegrate] = {"LocalVariables" -> {"Plot", {3, 3}}, 
   "ArgumentsPattern" -> {_, _, _}};

lineIntegrate[r_?VectorQ, f_Function, {t_, tMin_, tMax_}] := 
 Module[{param, localR}, localR = r /. t -> param;
  Integrate[(f[localR, #] Sqrt[#.#]) &@D[localR, param],
            {param, tMin, tMax}]]

lineIntegrate[{Cos[t], Sin[t]}, 1 &, {t, 0, 2 Pi}]

In Mathematica, we execute a file using the Get function. Here, we just use Clojuratica to call this on the appropriate filename:

user=> (math (Get "line-integral.m"))
(* 2 Pi)

This uses the Mathematica function Get, which takes the name of a file that contains one or more Mathematica commands. It executes those and returns the value of the last command.