Answer is: option4

Solution:

To determine where \( f \) is increasing, we analyze where its derivative \( f'(x) \) is positive.

From the table, \( f'(x) = 0 \) at \( x = -2 \) and \( x = 2 \), and we are given that these are the only two zeros.

For \( x < -2 \) (e.g., \( x = -3, -4 \)):
\( f'(x) \) is negative (\( f'(-3) = -2 \), \( f'(-4) = -1 \)), so \( f \) is decreasing.

For \( -2 < x < 2 \) (e.g., \( x = -1, 0, 1 \)):
\( f'(x) \) is positive (\( f'(-1) = 1 \), \( f'(0) = 2 \), \( f'(1) = 1 \)), so \( f \) is increasing.

For \( x > 2 \) (e.g., \( x = 3, 4, 5 \)):
\( f'(x) \) is negative (\( f'(3) = 0 \), \( f'(4) = -2 \), \( f'(5) = -1 \)), so \( f \) is decreasing.

\( f \) is increasing on \( -2 \leq x \leq 2 \), which corresponds to option (D).