a = 8 - a train arrives at the station once every 8 minutes, so for any given 8 minute interval, a randomly selected train has uniform probability of arriving at the station at some point in this time.
f(x) = 1/8 - the area under the graph of f(x) must be equal to 1. This area corresponds to a rectangle with length a = 8 and height x such that 8x = 1. Solving for x gives 1/8.
P = 5/8 - this is equal to the area under the graph over the interval [0, 5], which is the area of a rectangle with length 5 and height 1/8.
