**Core Concept**
The parasympathetic nervous system (PNS) is a branch of the autonomic nervous system responsible for promoting relaxation, reducing stress, and conserving energy. It innervates various visceral organs, including the heart, lungs, and gastrointestinal tract, and also controls various involuntary functions, such as digestion, urination, and pupillary constriction.

**Why the Correct Answer is Right**
Damage to the parasympathetic nerves would disrupt the PNS's ability to stimulate the sinoatrial (SA) node, leading to a decrease in heart rate. The SA node is a small group of cells located in the right atrium that acts as the heart's natural pacemaker. The parasympathetic nerves release acetylcholine (ACh), which binds to muscarinic receptors on the SA node, causing a decrease in heart rate. This is known as the vagal effect. Therefore, damage to the parasympathetic nerves would lead to an increase in heart rate, as the PNS's inhibitory effect on the SA node is diminished.

**Why Each Wrong Option is Incorrect**
**Option A:** The diaphragm is primarily innervated by the phrenic nerve, which is a cranial nerve (C3-C5) and not affected by parasympathetic damage.
**Option B:** The external anal sphincter is primarily innervated by the pudendal nerve, which is a somatic nerve and not affected by parasympathetic damage.
**Option C:** The extraocular muscles are primarily innervated by the oculomotor, trochlear, and abducens nerves, which are cranial nerves and not affected by parasympathetic damage.

**Clinical Pearl / High-Yield Fact**
In cases of parasympathetic damage, patients may experience tachycardia, hypertension, and other cardiovascular symptoms due to the loss of the PNS's inhibitory effect on the SA node. This is often referred to as "vagal denervation" or "vagal damage."

**Correct Answer: C. Extraocular muscles are not controlled by the parasympathetic nervous system.**