
theorem Th62:
for f be PartFunc of REAL,REAL, a,b,r be Real st ].a,b.[ c= dom f &
 f is_improper_integrable_on a,b holds
  -f is_improper_integrable_on a,b &
  improper_integral(-f,a,b) = - improper_integral(f,a,b)
proof
    let f be PartFunc of REAL,REAL, a,b,r be Real;
    assume ].a,b.[ c= dom f & f is_improper_integrable_on a,b; then
    (-1)(#)f is_improper_integrable_on a,b &
    improper_integral((-1)(#)f,a,b) = (-1) * improper_integral(f,a,b)
      by Th61;
    hence thesis by XXREAL_3:91;
end;
