
theorem Th56:
for f be PartFunc of REAL,REAL, a,b be Real st a < b & [.a,b.[ c= dom f &
 f is_right_improper_integrable_on a,b holds
   -f is_right_improper_integrable_on a,b &
   right_improper_integral(-f,a,b) = - right_improper_integral(f,a,b)
proof
    let f be PartFunc of REAL,REAL, a,b be Real;
    assume A1: a < b & [.a,b.[ c= dom f
      & f is_right_improper_integrable_on a,b;
    hence -f is_right_improper_integrable_on a,b by Th54;
    right_improper_integral(-f,a,b) = (-1) * right_improper_integral(f,a,b)
      by A1,Th54;
    hence right_improper_integral(-f,a,b) = - right_improper_integral(f,a,b)
      by XXREAL_3:91;
end;
