Cumulative distribution function integration

**The Question:**

The continuous random variable X has probability density function given by:

a) Sketch the graph of f.

b) Explain why the value of n, the median of X, is 1.

c) Show that the value of u, the mean of X, is .

d) Find P(X < 3u - n).

I've done a), b), and c), but am stuck on d).

**My Attempt:**

F(x) (the cumulative distribution function for X) is

, which becomes:

with limits 1 and x.

Substituting:

.

Now 3u - n = .

Hence =:

.

This works out to .

However, the actual answer is , and the cumulative distribution function F(x) is .

Some advice on how to proceed would be appreciated.

isx99