John Proctor shows his integrity by admitting to his wife that he was unfaithful. Although this took place some seven months prior to the beginning of the play, in Act Two, he references the fact that he did "confess" his infidelity to Elizabeth when she "told [him] [her] suspicion." He does seem to somewhat regret that decision now that he feels that Elizabeth continues to be suspicious of him, but he was honest nonetheless. His willingness to be honest when it could take such a toll on his relationship shows his integrity.
In addition, although John seems to still have feelings for Abigail, he is unwilling to be unfaithful to his wife again. When the two of them speak in private in Act One, he admits that "[he] may have looked up" at Abigail's window, missing her and wanting to be with her again, and that "[he] may think of [her] softly from time to time." However, he absolutely refuses to continue an affair with her because it would not be right. He says he would "cut off [his] hand" before he ever reaches to touch her again, and this shows his integrity as well.