theorem Th13: :: MESFUN15:11

for a, b being Real
for f being PartFunc of REAL,REAL st a <= b & [.a,b.] c= dom f & f | [.a,b.] is bounded & f is_integrable_on ['a,b'] & f | [.a,b.] is nonpositive holds
integral (f,a,b) <= 0