Thank you very much. I would like to learn more about integrals in equation 2, could you provide me with a reference to look at about methods used in eq. (2) please?

I understand that but what I fail to grasp is how the two parts of $\phi$ add up and become this term. I tried to follow along from the definition of fourier expansion of $\phi$ in 9.21 but I am probably too naive to see it...

Thanks loads! This does answer my question. So can I take this as a general method to solve questions like these? i.e Expand the time evolution operator in power series and try to separate out the even and odd parts and find a matrix representation of U?

sorry, i am not fully clear on what you are implying. Can you please elaborate on the steps to a solution?

well the first part of the question asked what are the possible values resulting from measurement of C and with what probabilities. that was simple enough