It may be that the microphone is bad. The 5C has two microphones one located at the bottom (used when making regular phone calls) and one up near the earpiece (used for facetime and speakerphone). First try putting the phone on speakerphone when making a call. If people are not able to hear you then you will most likely need to replace the microphone near the earpiece.
That microphone is located on the same flex cable as the front facing camera and proximity sensor.
iPhone 5c Front Camera and Sensor Cable
However, if people are able to hear you while using speakerphone then I would try a factory reset. This can either be done either in the settings menu or by putting your phone into dfu mode and connecting it to a computer with itunes installed. I would recommend the second way as it is a more complete reset which installs a fresh version of the OS as opposed to using the files that already exist on the phone. But either way, be sure to back up your data as it will be wiped during the process.
iPhone - 4 / 4S / 5 / 5S / 5c / 6 / 6S - How to flash in DFU mode