How much sleep should a 2 month old be getting during the day?

Well around that age they are starting to stay awake more during the day. I always let my baby who is 3 months just sleep when he wants he usually will wake up around 6 or 7 in the morning and then he will be back asleep around 8 or 9 for about an hour in half and then maybey another nap a few hours later and then around 5 he sleeps a little and then wakes up for bath time and his last feeding and then we put him to bed around 9 9:30 and he usually wakes up around 3 or 4 for a feeding but the last 2 night he has been sleeping through the whole night I get him up around 6 to get ready.