 reserve A for non empty Subset of REAL;
 reserve A for non empty closed_interval Subset of REAL;

theorem Lm21L:
  for a,b,c be Real st a < b & b < c holds
    TriangularFS (a,b,c) is_integrable_on A &
    TriangularFS (a,b,c) | A is bounded
proof
 let a,b,c be Real;
 assume A1: a < b & b < c;
 reconsider f = TriangularFS (a,b,c) as PartFunc of REAL,REAL;
 TriangularFS (a,b,c) is Lipschitzian by FUZZY_5:86,A1; then
 A6:f | A is continuous;
 dom f = REAL by FUNCT_2:def 1;
 hence thesis by INTEGRA5:11,INTEGRA5:10,A6;
end;
