Cumulative distribution function of a random variable x means :
If a value of a random variable is F(x) then it means probability the random variable takes any value <= x is given by F(x)..
So to find P(1/4 < x < 1) , we need to find F(1) and F(1/4) and then perform F(1) - F(1/4)..
So according to the piecewise definition of function given in the question :
F(1) = 3/4 [ Here we take 3/4 and not 1 bcoz we are asked the probability of x < 1 and not x <= 1 ]
F(1/4) = (1/4)2 = 1/16
Hence P(1/4 < x < 1) = 3/4 - 1/16
= 11/16
= 0.6875 = 0.69(correct to 2 decimal places)
Hence 0.69 should be the required probability..