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已知

f (x) = max {1, x^{2}}

, 则

\int f (x) d x =

A.

{\begin{cases} \frac{x^{3}}{3} - \frac{2}{3} + C, & x < - 1 \\ x + C, & - 1 \leq x \leq 1 \\ \frac{x^{3}}{3} + \frac{2}{3} + C, & x > 1 \end{cases}

B.

{\begin{array}{cc} \frac{x^{3}}{3} + C, & x < - 1 \\ x + C, & - 1 \leq x \leq 1 \\ \frac{x^{3}}{3} + C, & x > 1 \end{array}

C.

{\begin{array}{cc} \frac{x^{3}}{3} + C_{1}, & x < - 1 \\ x + C_{2}, & - 1 \leq x \leq 1 \\ \frac{x^{3}}{3} + C_{3}, & x > 1 \end{array}

D.

{\begin{cases} \frac{x^{3}}{3} - \frac{4}{3} + C, & x < - 1 \\ x + C, & - 1 \leq x \leq 1 \\ \frac{x^{3}}{3} + \frac{2}{3} + C, & x > 1 \end{cases}

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