Consider the following statements
1. Every function has a primitive
2. A primintive of a function is unique.
Which of the statements given above is/are correct?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Explanation

To analyze the given statements regarding primitive functions, we will evaluate each statement one by one.

### Step 1: Evaluate Statement 1
**Statement 1:** Every function has a primitive.

A primitive function (or antiderivative) of a function \( f(x) \) is a function \( F(x) \) such that \( F'(x) = f(x) \). However, not every function has a primitive. For example, functions that are not continuous on their interval may not have an antiderivative.

**Conclusion for Statement 1:** This statement is **false**.

### Step 2: Evaluate Statement 2
**Statement 2:** A primitive of a function is unique.

The uniqueness of a primitive function can be understood through the Fundamental Theorem of Calculus. If \( F(x) \) and \( G(x) \) are both primitives of \( f(x) \), then their difference \( F(x) - G(x) \) is a constant function. This means that while there can be multiple primitives, they differ by a constant. Therefore, we can say that the primitive is unique up to an additive constant.

**Conclusion for Statement 2:** This statement is **true**.

### Final Conclusion
From our evaluation:
- Statement 1 is false.
- Statement 2 is true.

Thus, the correct answer is that only the second statement is correct.

### Answer Summary
- **Correct Statements:** Only the second statement is correct.