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.