Is this Jeffrey Divergence code correct?

This function calculates a Jeffrey Divergence between 2 images histogram XI and XJ. I have Jeffrey Divergence function but it contains integration since I don't know how to code integration.

please help

function d=jeffrey_divergence(XI,XJ)
% Implementation of the Jeffrey Divergence
% (cf. "The Earth Movers' Distance as a Metric for Image Retrieval",
%      Y. Rubner, C. Tomasi, L.J. Guibas, 2000)
%
% @author: B. Schauerte
% @date:   2009
% @url:    http://cvhci.anthropomatik.kit.edu/~bschauer/

% Copyright 2009 B. Schauerte. All rights reserved.
% 
% Redistribution and use in source and binary forms, with or without 
% modification, are permitted provided that the following conditions are 
% met:
% 
%    1. Redistributions of source code must retain the above copyright 
%       notice, this list of conditions and the following disclaimer.
% 
%    2. Redistributions in binary form must reproduce the above copyright 
%       notice, this list of conditions and the following disclaimer in 
%       the documentation and/or other materials provided with the 
%       distribution.
% 
% THIS SOFTWARE IS PROVIDED BY B. SCHAUERTE ''AS IS'' AND ANY EXPRESS OR 
% IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 
% WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 
% DISCLAIMED. IN NO EVENT SHALL B. SCHAUERTE OR CONTRIBUTORS BE LIABLE 
% FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR 
% BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, 
% WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
% ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
% 
% The views and conclusions contained in the software and documentation
% are those of the authors and should not be interpreted as representing 
% official policies, either expressed or implied, of B. Schauerte.

m=size(XJ,1); % number of samples of p
p=size(XI,2); % dimension of samples

assert(p == size(XJ,2)); % equal dimensions
assert(size(XI,1) == 1); % pdist requires XI to be a single sample

d=zeros(m,1); % initialize output array

for i=1:m
  for j=1:p
    m=(XJ(i,j) + XI(1,j)) / 2;
      if m ~= 0  % if m == 0, then xi == xj == 0
        d(i,1) = d(i,1) + (XI(1,j) * log(XI(1,j) / m)) + (XJ(i,j) * log(XJ(i,j) / m));
      end
  end
end

Thanks