Mathematics

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 a.

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

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

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

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