There are two reasons why intestinal infection can bring on bloody stool.
First one, is the type of germ causing the intestinal infection (different germs are in different way pathogenic, or causing harm during intestinal infections).
Such germs are amoeba, intestinal parasite,
and some bacteria, Campylobacter, Salmonella, Shigella, Escherichia coli, damaging the cells that line the intestinal wall.
Another reason, are hemorrhoids that can be activated because of diarrhea,but, if you already suffer from hemorrhoids.
Diarrhea as constipation, cause hemorrhoids to relapse, and bleeding from them is seen as a bright red blood on the stool surface, on toilet paper or in a bowl.