Question

The difference between the maximum and minimum value of the function \[ f(x) = \int_{0}^{x} (t^2 + t + 1)\, dt \] on the interval \[ [2, 3] \] is: 

• A. \( \frac{39}{6} \)
• B. \( \frac{49}{6} \)
• C. \( \frac{59}{6} \)
• D. \( \frac{69}{6} \)
• E. \( \frac{79}{6} \)

Hint:

If \( f'(x) > 0 \) on an interval, the function is increasing, so minimum occurs at left endpoint and maximum at right endpoint.

Answer 1

The Correct Option is C