Decide whether the function $f(x)=\frac{12}{5}{x}^2-\frac{3}{10}$ is a probability density function on $-1,1.$ If not, tell why.

Is the function a probability density function on $[-1,1]?$

A$.$ No$,$ because ${\displaystyle \underset{-1}{\overset{1}{}}}(\frac{12}{5}{x}^2-\frac{3}{10})dx1.$

B$.$ No$,$ because $f(x)$ is not greater than or equal to $0$ for all $x$ in $-1,1.$

C$.$ Yes, the function is a probability density function on $-1,1.$