Normalized wavefunction

Consider a particle of mass m moving in a tube of length L. At time t=0, its normalized wavefunction is

psi(x,0)=(8/5L)^(1/2)*(1+cos(pi*x/L))*sin(pi*x/L)

inside the well (0<=x<=L) and zero outside. (Hint, look for trig identities, as a superposition of eigenstates)

a. If the energy of the probability is measured , what possible energies could be found, and what are the probabilities of each?

b. From the answers in part (a), compute (E) ( without doing any integrals), and find the wavefunction psi(x,t) at any later time t>0.

c. What is the probability that the particle is found in the left half of the tube
(0<=x<= L/2) at time t?