Lời giải
• \( x^2 - 2x + 2 = x^2 + 4x + 5 \Leftrightarrow x = -\frac{1}{2} \)
\( S = S_1 + S_2 = \int_{-2}^{\frac{-1}{2}} \big( x^2 + 4x + 5 - 1 \big) \, dx + \int_{\frac{-1}{2}}^1 \big( x^2 - 2x + 2 - 1 \big) \, dx \)
\( = \int_{-2}^{\frac{-1}{2}} \big( x^2 + 4x + 4 \big) \, dx + \int_{\frac{-1}{2}}^1 \big( x^2 - 2x + 1 \big) \, dx \)
\( = \left( \frac{x^3}{3} + 2x^2 + 4x \right) \bigg|_{-2}^{\frac{-1}{2}} + \left( \frac{x^3}{3} - x^2 + x \right) \bigg|_{\frac{-1}{2}}^1 \)
\( = \frac{9}{4} \) (đvdt)
Bấm
\( \int_{-2}^{\frac{-1}{2}} \big( x^2 + 4x + 1 \big) \, dx + \int_{\frac{-1}{2}}^1 \big( x^2 - 2x + 1 \big) \, dx = \frac{9}{4}\)
\(\Rightarrow\) Vậy chọn đáp án \(\boxed{\text{C}} \)