Is there a pullup on I2C? I am using an Arduino Uno R3.

It is not clear on the schematic whether there are pullups on the A4 and A5 I2C pins.

Are there hardwired pullups or do I have to add them myself?
There are very weak internal pullups, but they are not strong enough to be considered compliant with I2C specs. Supply your own external 2.2k-10kohm pullup resistors.