Here is one that represents God's will for his children.
"My son, if thou wilt receive my words, And lay up my commandments with thee; So as to incline thine ear unto wisdom, And apply thy heart to understanding; Yea, if thou cry after discernment, And lift up thy voice for understanding; If thou seek her as silver, And search for her as for hid treasures: Then shalt thou understand the fear of Jehovah, And find the knowledge of God." (Proverbs 2:1-5 ASV)
I don't see any integrity in this. I don't see a person using their own reasoning faculties to assess and decide if what they are hearing from God makes sense. This is about accepting God even before God says anything. Like an obsequious puppy dog receiving a treat only after it cowered in fear before us.
How can anyone with integrity make up their mind God is right BEFORE they hear what God has to say?
Speaking for myself, I was taught to believe before I even knew much about the scriptures. I was fertile ground because of innocence and childhood brainwashing. As I grew I didn't actively decide to see problems with religion. I wasn't even looking for them. The problems just became plain obvious and nothing I could do - not even heartfelt prayer - produced any answers from God. The "knowledge of God" in Proverbs 2:1-5 was withheld from me. It's a lie to me.
I did nothing other than use my brain (which I thought was God-given) so see the massive problems in religion and scriptures. Would I have any integrity if I shut out those thoughts without looking for more information? What should I do if what I find confirms that the problems and inconsistencies are real? Suppress it because I'm scared of God? No! I'm not a coward.
And back to the point of the OP, this same experience of dissonance between scriptures and reality (I think) is the main reason people disobey Jesus (and God). The scriptures just don't make sense when you take them seriously:
Why would anyone hate their family, and abandon them?
Why would anyone sell all their stuff and give it all away?
Why would we not feel relieved, even happy, that Osama Bin Laden was shot dead?
Why do we save for our retirement?
Why would anyone mutilate themselves because they thought somebody looks sexy?
Why are we (most of us) afraid of handling snakes?
Why do we label poisons as poisons and avoid ingesting them?
Why do we take our injured loved ones to hospitals and doctors instead of prayer groups?
Blind faith in Jesus or God's "Word" is patently dangerous and stupid. We'd have ZERO integrity accepting what scriptures say with respect to any of the above. We'd have ZERO integrity if we didn't question EVERYTHING else in the same book the above nonsense appears in.
I can conclude only one thing, that if there is a god of some description out there it cannot possibly be BibleGod.