How can I tell whether or not a function f can be a probability density function?

Question

Consider the function:

$ f(x)= \begin{cases} c(2x - x^3),& 0<x\lt \frac{5}{2}\\ \\ \;0 &\text{otherwise}\\ \end{cases} $

I need to determine whether or not this can be a probability density function. My first step was to find $C$, by taking the integral of the function $c(2x - x^3)$, from $\frac{5}{2}$ to $0$, and setting it equal to 1 to find $C$.