First order correction

For simple harmonic oscillator H = p^2/(2m) + (K/2)x^2 turn on
the potential V(x) = cx^4

Calculate the first order correction to the ground state energy.

Prove that the first order energy correction vanishes for all n = odd integer excited state levels.

Please do this in full detail as it is a problem that I was able to do two years ago but have now forgoten and need to know it again...thank you!!!