function[I21Lower, I21ttLower, I21xxLower, I21xtLower, I21txLower, I21x1Lower, I21x2Lower, I21t1Lower, I21t2Lower]=IDataTable21ULower (x1, x2, t1, t2, mR, mL, kappa)
I21Lower=@(omega,t)omega.^(-1).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*cos(omega.*(t1+( ...
  -1).*t2)).*coth(kappa.^(-1).*omega.*pi).*((mL.^2+omega.^2).^(1/2) ...
  .*cos(omega.*xstar1).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+omega.* ...
  sin(omega.*xstar1).*sin((mL.^2+omega.^2).^(1/2).*xstar2));

I21ttLower=@(omega,t)omega.*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*cos(omega.*(t1+(-1).* ...
  t2)).*coth(kappa.^(-1).*omega.*pi).*((mL.^2+omega.^2).^(1/2).*cos( ...
  omega.*xstar1).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+omega.*sin( ...
  omega.*xstar1).*sin((mL.^2+omega.^2).^(1/2).*xstar2));

I21xxLower=@(omega,t)pi.^(-1).*cos(omega.*(t1+(-1).*t2)).*coth(kappa.^(-1).*omega.*pi) ...
  .*(omega.*cos(omega.*xstar1).*cos((mL.^2+omega.^2).^(1/2).*xstar2) ...
  +(mL.^2+omega.^2).^(1/2).*sin(omega.*xstar1).*sin((mL.^2+omega.^2) ...
  .^(1/2).*xstar2));

I21xtLower=@(omega,t)omega.*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*coth(kappa.^(-1).* ...
  omega.*pi).*sin(omega.*(t1+(-1).*t2)).*((-1).*(mL.^2+omega.^2).^( ...
  1/2).*cos((mL.^2+omega.^2).^(1/2).*xstar2).*sin(omega.*xstar1)+ ...
  omega.*cos(omega.*xstar1).*sin((mL.^2+omega.^2).^(1/2).*xstar2)); ...
  

I21txLower=@(omega,t)pi.^(-1).*coth(kappa.^(-1).*omega.*pi).*sin(omega.*(t1+(-1).*t2)) ...
  .*((-1).*omega.*cos((mL.^2+omega.^2).^(1/2).*xstar2).*sin(omega.* ...
  xstar1)+(mL.^2+omega.^2).^(1/2).*cos(omega.*xstar1).*sin((mL.^2+ ...
  omega.^2).^(1/2).*xstar2));

I21x1Lower=@(omega,t)(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*cos(omega.*(t1+(-1).*t2)).* ...
  coth(kappa.^(-1).*omega.*pi).*((-1).*(mL.^2+omega.^2).^(1/2).*cos( ...
  (mL.^2+omega.^2).^(1/2).*xstar2).*sin(omega.*xstar1)+omega.*cos( ...
  omega.*xstar1).*sin((mL.^2+omega.^2).^(1/2).*xstar2));

I21x2Lower=@(omega,t)omega.^(-1).*pi.^(-1).*cos(omega.*(t1+(-1).*t2)).*coth(kappa.^(-1) ...
  .*omega.*pi).*(omega.*cos((mL.^2+omega.^2).^(1/2).*xstar2).*sin( ...
  omega.*xstar1)+(-1).*(mL.^2+omega.^2).^(1/2).*cos(omega.*xstar1).* ...
  sin((mL.^2+omega.^2).^(1/2).*xstar2));

I21t1Lower=@(omega,t)(-1/4).*(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*csch(kappa.^(-1).* ...
  omega.*pi).^2.*((mL.^2+omega.^2).^(1/2).*cos((mL.^2+omega.^2).^( ...
  1/2).*xstar2).*(sin(omega.*(t1+(-1).*t2+(-1).*xstar1))+sin(omega.* ...
  (t1+(-1).*t2+xstar1)))+omega.*(cos(omega.*(t1+(-1).*t2+(-1).* ...
  xstar1))+(-1).*cos(omega.*(t1+(-1).*t2+xstar1))).*sin((mL.^2+ ...
  omega.^2).^(1/2).*xstar2)).*sinh(2.*kappa.^(-1).*omega.*pi);

I21t2Lower=@(omega,t)(mL.^2+omega.^2).^(-1/2).*pi.^(-1).*coth(kappa.^(-1).*omega.*pi).* ...
  sin(omega.*(t1+(-1).*t2)).*((mL.^2+omega.^2).^(1/2).*cos(omega.* ...
  xstar1).*cos((mL.^2+omega.^2).^(1/2).*xstar2)+omega.*sin(omega.* ...
  xstar1).*sin((mL.^2+omega.^2).^(1/2).*xstar2));
