If $G(x)$ be the distribution function of random variable $X$ symmetric about $0$ then $\int_{-a}^{a} G(x)dx$ equals
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For any CDF $F(x)$ symmetric about $0$, the area under the curve from $-a$ to $a$ is always equal to $a$. This is a very useful shortcut in probability theory problems involving integration of symmetric CDFs.