Cancelling the card or paying off the balance will rid you of bad history

Your payment history makes up 35 percent of your FICO score and closing the accounts with less than perfect histories will not make the harmful information go away. While paying off the balance is a good thing and can boost other areas affecting your score, it will still not remove the dark marks highlighting your payment history.

How it can cause more damage:

Cancelling the account does not remove the late payments associated with it. What it does is, it affects your debt-to-credit ratio (unless you make payments on your other debt to make up as well) and it can also affect the length of your credit history, especially if it’s an old account.

If the adverse information is not correct, be sure to contest it. But if it has been reported correctly, the best thing to do is to pay the credit cards on time, even if it is the minimum payment. Use the card to start building a good solid history of making timely payments and eventually, it will have a positive affect on your score.