mixed type distribution

[N]

Let x be a random variable of the mixed type having the distributions function

F(x)=         0    if x<0
                 x^2/4   if 0 is less than and equal to x <1
                 (x+1)/4   if 1 is less than equal to x  and < 2
                 1              2 is < and = to x

find mean of x
and probability at x =1/2