I am in a similar situation, except it is for a 1099-INT that was not postmarked until 2/9! It is for an account I completely forgot I even had - it was only open 2 months but did generate ~$30 in interest.
Since I didn't receive it until so late, I already filed. I obviously still owe my $6 tax or whatever, but what happens when a 1099 is mailed after the 1/31 cutoff?
But it doesn't work just like that.
You are taxed based on your 'taxable income'. The tax amount only changes at every $50.
But, a $1 increase can change your taxes by quite a bit;
If your taxable income is $50,000; tax for a joint return is $6.569
Joint return tax for taxable income of $50,001 is $6,576 - an increase of $7.
Re-calculate your taxes with the interest income. If you do owe more, do an online payment. Do thorough documentation.