Consider continuous functions f on the interval [0,1] which statisfy the following two conditions:

i) f (x) <= (5)^(1/2) for all x belonging to [0,1]

ii)  f (x) <= 2/x for all x belonging to [0, 1/2]

Then, the smallest real number a such that the inequality integration of f(x)dx running from 0 to 1 , is less than equal to a.