Peristomium is the segment of an earthworm that bears the mouth. Let's understand why this is the correct answer.

# Earthworm Anatomy
An earthworm's body is divided into several segments called metameres. Each metamere is similar in structure and function, and they are arranged in a linear series from the anterior (head) to the posterior (tail) end of the worm. The mouth is located on the anterior end of the earthworm's body.

# Peristomium
The segment of an earthworm that bears the mouth is known as the peristomium. It is the first segment of the worm's body and is located right behind the prostomium.

# Prostomium
The prostomium is the part of an earthworm's body that covers the mouth. It is a small, fleshy lobe or lobe-like projection that extends over the mouth. While the prostomium covers and protects the mouth, it does not bear the mouth itself.

# Deuterostomium and Stomium
The options "Deuterostomium" and "Stomium" are not correct in this context.
- Deuterostomium refers to the second opening formed during embryonic development in organisms with deuterostome development, such as chordates. It is not related to the segment bearing the mouth in an earthworm.
- Stomium is not a recognized anatomical term in relation to earthworms or their mouth-bearing segment.

Therefore, the correct answer is option C) Peristomium, as it correctly identifies the segment of an earthworm that bears the mouth.