If the distribution function of random variable x is f (x) = a + barctanx, then a =?

If the distribution function of random variable x is f (x) = a + barctanx, then a =?

F(-∞) = a- π/2 · b =0
F(+∞) = a+ π/2 · b =1
We can get a = 1 / 2, B = 1 / π
a=1/2