integrity is the number of creatures you have in the ritual, the fact you only have two bars is normal for the fact you only have two creatures in it
it will not defend on it's own? you mean a random ritual is selecected when you're attacked?
check both these options, is your ritual still intact? as in if you click to attack someone are you able to select that rit to attack with? if the ritual has been defeated and is no longer intact, then a random rit will be selected for you
and does the ritual have over 300 creature vitality in it? if your barron souls have less than that because they've suffered damage in previous battles, then again a random ritwill be selected