Magnetic Field for straight wire loop

Dear all,

I have a program that will use the Biot-Savart's law to calculate the magnetic field for my square loop. The problem I am having is when I done the integral:

(y-yp)/sqrt(r^2+(y-k)^2)^3 dy from y= -a to a ==> -1/ sqrt((yp-y)^2+r^2).

And for the program to work I have to have:

-1/ sqrt((yp-a)^2+r^2) - 1/ sqrt((yp+a)^2+r^2)

instead of the right way of integral:

-1/ sqrt((yp-a)^2+r^2) + 1/ sqrt((yp+a)^2+r^2).

In the program the wire is in the y direction and magnetic field calculated for x and z direction.

My question how come the normal integration will not work with the program.

Also a is the length of the wire and values divided for thousand because those are in mm and in my script values entered in m.

function [Bx,Bz]=m_field(I,a,x0,y0,z0,z,xmin,ymin,xmax,ymax,step)

%miu0=4*pi*10^-7;
miu0=1.25664E-6;
B0=(I*miu0)/(4*pi);
a=a/1000;

in1=1;
for x=xmin:step:xmax

      in2=1;
      for y=ymin:step:ymax

          if (!(x==x0 & z==z0))
             r=(sqrt((x-x0)^2+(z-z0)^2))/1000;
             yp=(y-y0)/1000;
       Bn=B0*((-1/sqrt(r^2+(yp-a)^2)) - (1/sqrt(r^2+(yp+a)^2)));   
       Bx(in1,in2)=(B*((z-z0)/1000/r));
             Bz(in1,in2)=(B*((x-x0)/1000)/r);
          else
             Bx(in1,in2)=0;
             Bz(in1,in2)=0;
          end
          X(in1,in2)=x;
    Y(in1,in2)=y;
          in2=in2+1;    
      end
      in1=in1+1;
  end

s=size(Bx);
for i=2:s(1)-1
    for j=2:s(2)-1
        if (Bx(i,j)==0 & Bz(i,j)==0)   
           Bz(i,j)=1/8*(Bz(i-1,j-1)+Bz(i-1,j+1)+Bz(i-1,j)+Bz(i,j-1)+Bz(i,j+1)+Bz(i+1,j-1)+Bz(i+1,j+1)+Bz(i+1,j));
        end
    end
end