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If f is continuous function then which of the following is correct

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$\int_{- 2}^{2} f (x) d x = \int_{0}^{2} (f (x) - f (- x)) d x$

$\int_{- 3}^{5} 2 f (x) d x = \int_{- 6}^{10} f (x - 1) d x$

$\int_{- 3}^{5} f (x) d x = \int_{- 6}^{10} f (\frac{x}{2}) d x$

$\int_{- 3}^{5} f (x) d x = \int_{- 2}^{6} f (x - 1) d x$

answer is D.

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Detailed Solution

$\int_{a + c}^{b + c} f (x) dx = \int_{a}^{b} f (x + c) dx \int_{- 3}^{5} f (x) dx = \int_{- 3 + 1}^{5 + 1} f (x - 1) dx = \int_{- 2}^{6} f (x - 1) dx$

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