Correct Answer: (E)
There are two parts to this sentence: a dependent clause beginning with the word "despite" and an independent clause, which begins after the comma. In order to find the right answer, you first must figure out how these two sentences are related. The first clause has the word "despite," so we know the meaning of the first blank will be different than that of the second. Next, there is some important information in the second clause because we know that Julia would not go along with cheating just because her friends are doing it. This second blank should contain a word that goes along with the idea of having honesty.
You can eliminate (C) "adversity," which means "misfortune," as well as (B) "longevity" since "lifespan" is not related to being honest. (A) "theory" doesn't really have anything to do with being honest, so we are left with (D) and (E). "Integrity" (E) sounds like the better choice, but first let's have a look at that first blank. The second part of the sentence gives us a bit of clue here as well: Julia would not "go along with" her friends." (D) "compassion" means "caring," but (E) "conformity" looks like it is a much better fit. The correct answer is (E) since "conformity" means "compliance" and "integrity" is "honesty."