K[x_, psi_] :=
Evaluate@FullSimplify@
Sum[Sin[n*Pi*x]*
Sin[n*Pi*
psi]*(2*Exp[-(n*Pi)^2*
Abs[s + r]] - (Exp[-(n*Pi)^2*Abs[s - r]] -
Exp[-(n*Pi)^2*(s + r)])/(n*Pi)^2), {n, 1, j}];
TL[x_, psi_] := Evaluate@Chop@Integrate[K[x - y, psi]*y, {y, -10, 10}];
TU[x_, psi_] :=
Evaluate@Chop@Integrate[K[x - y, psi]*(1 - y), {y, -10, 10}];