Probability density function in details

If the function for the PDF is given by:

$$f_X(x) = \Big\{ \begin{array}{lr} \frac{6}{125}x(5-x) & \text{when } 0\leq y \leq 5\\ 0 & \text{otherwise } \end{array}$$Calculate the probability of the continuous random variable $Z$, given $0 \leq Z \leq 1$ and $2 \leq Z \leq 3$

Tip: Additivity rule for independent events