What is the sun of the polynomials 3x^2+2x+1 and 2x^2-x+4?

To find the sum of the polynomials \(3x^2 + 2x + 1\) and \(2x^2 - x + 4\), we will add them together by combining like terms.

1. **Combine the \(x^2\) terms:**
\[
3x^2 + 2x^2 = 5x^2
\]

2. **Combine the \(x\) terms:**
\[
2x - x = x
\]

3. **Combine the constant terms:**
\[
1 + 4 = 5
\]

Now, combine all these results:
\[
5x^2 + x + 5
\]

Thus, the sum of the polynomials is \(5x^2 + x + 5\).

**The correct answer is A: \(5x^2 + x + 5\)**.