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

theorem Lm22c:
  for a,b,c,d be Real st a < b & b < c & c < d holds
    TrapezoidalFS (a,b,c,d) is_integrable_on A &
    TrapezoidalFS (a,b,c,d) | A is bounded
proof
 let a,b,c,d be Real;
 assume A1: a < b & b < c & c < d;
 reconsider f = TrapezoidalFS (a,b,c,d) as PartFunc of REAL,REAL;
 TrapezoidalFS (a,b,c,d) is Lipschitzian by FUZZY_5:87,A1; then
 A6:f | A is continuous;
 dom f = REAL by FUNCT_2:def 1;
 hence thesis by INTEGRA5:11,INTEGRA5:10,A6;
end;
