The area under the graph of the probability density function
between $x=a$ and $x=b$ gives the probability that the outcome is
between $a$ and $b$ so the total area under the graph must be $1$,
in this example for $x$ between $0$ and $3$.

To find the median we have to find the value $t$ such that the area under the graph for $0\leq x \leq t$ is $0.5$. You will have to find the roots of a cubic equation (which you should be able to factorise) in this example and then identify the root which lies in the required interval.

To find the median we have to find the value $t$ such that the area under the graph for $0\leq x \leq t$ is $0.5$. You will have to find the roots of a cubic equation (which you should be able to factorise) in this example and then identify the root which lies in the required interval.