I have two 1099-INTs from same institution, do I simply sum the total and enter as one 1099-INT?

Each 1099-INT should be entered separately, even if they are from the same institution/bank and for different accounts. I also ran into this with 1099-R forms, and although the payer-ID is the same number, the addresses are different. 

Entering each separately makes it easier for the IRS computers to match what you report to what was reported to them. 

This year I have two 1099-INTs from one bank; one form reports interest on two different accounts; the other form reports interest on one account.  I added the three together as one payer on my TurboTax return.  I have done this for several years & I have never had a question raised by the IRS & refunds have been fast.  The total amount is not very significant to my total income.