For a function f ( x ), which of the following holds true?

$\displaystyle \int_{a}^{b} \mathrm{f}(\mathrm{x}) d \mathrm{x}=\int_{a}^{b} \mathrm{f}(a+b-\mathrm{x}) d \mathrm{x}$

$\displaystyle \int_{-a}^{a} \mathrm{f}(\mathrm{x}) d \mathrm{x}=0$, if $\displaystyle \mathrm{f}$ is an even function

$\displaystyle \int_{-a}^{a} \mathrm{f}(\mathrm{x}) d \mathrm{x}=2 \int_{0}^{a} \mathrm{f}(\mathrm{x}) d \mathrm{x}$, if $\displaystyle \mathrm{f}$ is an odd function

$\displaystyle \int_{0}^{2 a} \mathrm{f}(\mathrm{x}) d \mathrm{x}=\int_{0}^{a} \mathrm{f}(\mathrm{x}) d \mathrm{x}-\int_{0}^{a} \mathrm{f}(2 a+\mathrm{x}) d \mathrm{x}$