If X is a continuous random variable having distribution function F

If X is a continuous random variable having distribution function F , then its
median is defined as that value of m for which
F (m) = 1/2
Find the median of the random variables with density function
a)f (x) = 1, 0 ≤ x ≤ 1.

well this is easy:

F(x) = integral ( f(y) dy ) from y = 0 to x

So F(x) = integral( dy ) from y = 0 to x
F(x) = x + constant but the constant = 0 by normalization F(1) = 1

so F(x) = x = 1/2 has the solution x = 1/2