The Macmillandictionary says it is, but I'm still unsure about its veracity.
The sentence in which I'd like to use it, is as follows :
"Sometimes peer-pressure & the feeling of need to conform can hinder a person from remaining
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"Valid" is a subjective thing here. It's obviously a valid adjective - although the spelling integrous seems to have significantly more use - but your question seems to be "is the word in common use?"
The answer to this is no. As a native speaker, I don't recall ever hearing it being used. Instead you will likely opt for a description that involves its noun counterpart:
He is a man [of/with] great integrity.
Adjectival scenarios will tend to use a synonym or similar word to define the characteristics:
He is an honest, trustworthy man [of great integrity].