**Core Concept**
Perineal tears are classified based on the severity and extent of the damage to the perineal muscles and mucosa. The classification system helps in assessing the severity of the injury and guiding the management.

**Why the Correct Answer is Right**
This type of perineal tear is classified as a third-degree tear. The tear extends through the sphincter of the rectum, but the rectal mucosa is intact. This indicates a partial disruption of the anal sphincter, which is a hallmark of a third-degree tear. The presence of intact rectal mucosa is a distinguishing feature from a fourth-degree tear, where the mucosa is also involved.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because a first-degree tear only involves the skin and perineal muscles, without extending to the anal sphincter.
**Option B:** This option is incorrect because a second-degree tear involves the perineal muscles, but not the anal sphincter, whereas the tear in question extends through the sphincter of the rectum.
**Option C:** This option is incorrect because a fourth-degree tear involves the anal sphincter and the rectal mucosa, whereas the rectal mucosa is intact in this case.

**Clinical Pearl / High-Yield Fact**
It is essential to accurately classify perineal tears to ensure proper management and prevent long-term consequences, such as fecal incontinence.

**Correct Answer:** C.