Which sentence has a misplaced modifier?
i am definitely going to be ordering dessert after this delicious meal.
the boys were grateful that their father had paid for dinner for all of them.
bringing the check to the table, the boys were happy to see the waiter.
after they read the menu for a few minutes, the boys decided to order dinner.

The answer to your question would be that the sentence that has a misplaced modifier is the following one: Bringing the check to the table, the boys were happy to see the waiter.

A misplaced modifier is a word, phrase or clause that is separated from the word it modifies/describes. Consequently, the sentences sound awkward and even confusing.  However, more specifically, the example in question would be a case of a dangling modifier. Dangling modifers are a phrase or clause that is not logically related to the word/words it modifies.

In the example, the sentence does not specify who is bringing the check to the table. Yet, since it is next to "the boys were happy to see the waiter" and because we know what waiters do, the sentence suggests that the waiter is the one bringing the check.

- "the basic difference between keywords and subjects is that subjects (or "subject headings") have been predetermined, while keywords have not. a keyword is an easy place to start because you can use any word that seems to fit your search; this is called "natural language" searching."