If the amount that was not reported on your return is significant enough to make a change in your taxes, then you would receive a notice from the IRS for under-reporting your income. Part of the notice would include any changes they made to your return to add the income and recalculate your taxes. Generally, you would also see an amount that you owe due to the change.
If the amount that was not included was small enough that you did not receive a Form 1099-INT, you will probably not be contacted by the IRS with a notice, especially since it should be exempt from taxes in your case.
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