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What is an example of integral domain that is not a division ring?

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    @Lmn6 Not a well posed question.2011-09-30

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What is the first ring that pops into your head when you think of a ring? Is it a division ring? No! Is it an integral domain? Yes!

Methinks you just need to learn your definitions...

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Hint: think about the word integral

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    @Chris: was that intended for me or Swlabr? If for Swlabr, using $\mathrm{@Swlabr}$ notifies Swlabr.2011-09-30
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In a division ring every non zero element is a unit. The only units in $\mathbb{Z}$ are $1$ and $-1$, so $\mathbb{Z}$ is not a division ring but an integral domain.