Neither is correct. If you don't know whether this article is out of date, then look at the dateline at the top right corner of the page. if --> whether, "look" --> "look at", look for If you don't know whether this article is out of date, then see the dateline at the top right corner of the page. - less likely, but could be said.

THank you

If you don't know if the article is out of date or not, then look at/check/see the dateline at the top right corner of the page. All 3 options would be right. "See" is more likely to be heard in a educational setting (a professor speaking to a class) than in casual conversation, in my experience (American speaker of English).