(2014.A)

Lời giải

  \( x^2 - x + 3 = 2x + 1 \)  \( \Rightarrow x^2 - 3x + 2 = 0 \)   \( \Leftrightarrow \left[
\begin{array}{l}
x = 1 \\
x = 2
\end{array} \right. \)

  \( S = \int_{1}^{2} \left[ (x^2 - x + 3) - (2x + 1) \right] dx \)   \( = \int_{1}^{2} |x^2 - 3x + 2| dx \)  
      \( = \left| \int_{1}^{2} (x^2 - 3x + 2) dx \right| \)   \( = \left| \left( \frac{x^3}{3} - \frac{3x^2}{2} + 2x \right) \Big|_{1}^{2} \right| \)  
      \( = \frac{1}{6} \)