You go through TSA screening after you check in at IND. At check-in your bags will be bar-coded and tagged and will not be seen again until you reach Rome. Then you go through Italian Customs - as you enter the country.
On leaving Rome, you will again go through screening security. Your bags will be tagged for IND but on entering the US at JFK you will need to collect them, go through Customs and Immigration and then outside the Customs hall will be an area where you deposit your luggage for onward flights..
Check your tickets for differing terminals. Most commonly all the domestic flights go out of one terminal and all International leave from another, you may have to get internal train to connect over or walk...
These instructions apply to having the same airline for each flight!!
If you have booked different airlines for each leg of your flight, ask at the check in desk what you need to do re luggage.