for f, g being PartFunc of REAL,REAL
for a, b being Real st a < b & [.a,b.[ c= dom f & [.a,b.[ c= dom g & f is_right_ext_Riemann_integrable_on a,b & g is_right_ext_Riemann_integrable_on a,b holds
( f + g is_right_ext_Riemann_integrable_on a,b & ext_right_integral ((f + g),a,b) = (ext_right_integral (f,a,b)) + (ext_right_integral (g,a,b)) )