Jonas shows intelligence because he is aware of what is happening around him, even from a young age and in a community where no one seems to think for oneself. For example, Jonas is heavily concerned with using the right word to describe his feelings. Jonas also does well in his studies, according to his father.
Integrity is a concept beyond honesty. It is defined as "moral character" (dictionary.com). Jonas is watched all of the time, as everyone in the community is, but he also tries hard to obey the rules and tell the truth because he thinks it's the right thing to do. When he is asked to put the apple back, he does.
Courage is a trait that Jonas acquires, but he does seem brave to embark on the confusing and scary process of becoming Receiver of Memory. He accepts the painful memories and rise to learn from them. When Jonas leaves with Gabe, he shows true courage.
"The fourth essential attribute," the Chief Elder said, "is wisdom. Jonas has not yet acquired that. The acquisition of wisdom will come through his training.
Wisdom is the idea of seasoned intelligence to make good decisions. The Elders say that Jonas will acquire wisdom, but he seems to already have it. He realizes that the memories are important to the community, and that the fact that people don't feel is wrong. He knows that the communities concept of releasing anyone who doesn't fit in is wrong, and he works to rectify this.
Lowry, Lois (1993-04-26). The Giver (Newbery Medal Book) (p. 63). Houghton Mifflin Harcourt. Kindle Edition.