Which of the following correctly simplifies (9x^2 + 17x + 13) - (2x^2 + 12x + 11)?

To simplify the expression \((9x^2 + 17x + 13) - (2x^2 + 12x + 11)\), we start by distributing the negative sign to each term in the second parentheses:

\[
(9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11
\]

Now we can combine like terms:

1. For the \(x^2\) terms:
\[
9x^2 - 2x^2 = 7x^2
\]

2. For the \(x\) terms:
\[
17x - 12x = 5x
\]

3. For the constant terms:
\[
13 - 11 = 2
\]

Putting it all together, we have:

\[
7x^2 + 5x + 2
\]

Thus, the expression simplifies to:

\(\boxed{7x^2 + 5x + 2}\)