my phone's screen comes on when I receive a call

[qurk]

Basically, my problem is that my phone's screen comes on when I receive a call, and stays on. It's a problem because if it's sitting in my pocket in my coat while I'm at work, the battery drains so quickly after I get a call and get back to the phone, sometimes hours later. The only way really I have modified my phone is by installing a "call announce" app which has the phone speak who is calling...but I don't see how it could be the culprit. Anyone have any ideas how I can set my phone to not turn on screen when I get a call? Loving my Droid 4, had it for 3 months now.