S2 Edexcel Rectangular Uniform Distribution help!

Q: https://gyazo.com/f033abbe5197078acbb3f527c67ac7e9
A: https://gyazo.com/fdf85b44a6e85a25510cb07b4780157b
Can you please explain question D, I don't get how E(R) is related to Var(X) and E(X^2). Also can you explain the alternate method too? Thanks in advance

Surely you should know that since $R = 9X - X^2$ then

.

So since $\text{Var}(X) = E(X^2) - E(X)^2 \Rightarrow E(X^2) = \text{Var}(X) + E(X)^2$.

Plugging this into the previous equation yields $E(R) = 9E(X) - (\text{Var}(X) + E(X^2)) = \cdots$

The alternative method is just using the fact that $E(g(X)) = \int_{-\infty}^{\infty} g(x)f(x) \, \mathrm{d}x$.

You really need to include more of your own thoughts and attempts instead of just asking for an explanation. Keep that in mind next time.