Answer is: option2
\( \frac{253}{12} \)Solution:
Area = \[ \int_{-2}^3 \left| x^3 - x^2 - 6x \right| \, dx = \left| \left[ \frac{x^4}{4} - \frac{x^3}{3} - 3x^2 \right]_{-2}^0 \right| + \left[ \frac{x^4}{4} - \frac{x^3}{3} - 3x^2 \right]_0^3 \]
\[ = \left| \frac{16}{3} \right| + \left| \frac{-63}{4} \right| = \frac{16}{3} + \frac{63}{4} = \frac{253}{12} \]
So, the correct answer is (B) \( \frac{253}{12} \).