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Definite Integrals and Function Symmetry
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Let $$t$$ be a function such that $$t(-x) = -t(x)$$ for all $$x$$. If $$\displaystyle\int_1^3 (t(x) + x^2)\,dx = 18$$, then $\displaystyle\int_{-3}^{-1} (t(x) + x^2),dx =\ ?

Let $$t$$ be a function such that $$t(-x) = -t(x)$$ for all $$x$$. If $$\displaystyle\int_1^3 (t(x) + x^2)\,dx = 18$$, then $$\displaystyle\int_{-3}^{-1} (t(x) + x^2)\,dx =\ ?$$

A

$$\displaystyle -\frac{2}{3}$$

B

$$\displaystyle 18$$

C

$$\displaystyle -18$$

D

$$\displaystyle \frac{2}{3}$$

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