Verify that the function below is a probability density function for a continuous random variable X over the given interval. Determine the specified probability.

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and ${\displaystyle \underset{-}{\overset{\phantom{}}{}}}dx{\displaystyle \underset{2}{\overset{\phantom{}}{}}}dx=$

B$.$ The function is a probability density function because $f$ is continuous on the given interval, $f$ is nonnegative, and ${\displaystyle \underset{-}{\overset{2}{}}}|,|dx{\displaystyle \underset{2}{\overset{}{}}},|dx|=$

$$ C$.$ The function is a probability density function because $f$ is continuous, except at a finite number of points, $f$ is nonnegative, and ${\displaystyle \underset{-}{\overset{2}{}}}dx{\displaystyle \underset{2}{\overset{}{}}}dx=$