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 £ x £ 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.