The value of (where denotes the greatest integer function) is equal to

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The value of

\int_{0}^{2} \lfloor x^2 - x + 1 \rfloor \, dx

(where

\lfloor \cdot \rfloor

denotes the greatest integer function) is equal to (1)

\frac{5 + \sqrt{5}}{2}

(2)

\frac{1 + \sqrt{5}}{2}

(3)

\frac{1 - \sqrt{5}}{2}

(4)

\frac{5 - \sqrt{5}}{2}