How are mean and variance calculated in Bayesian curve fitting? This page is from Pattern Recognition by Bishop. What is the explanation for equations 1.70. 1.71 and 1.72?

Edit: The distributions are all Gaussian.
Since you only mention that their Gaussian, here is a screenshot depicting the relationship of gaussian conjugate priors  



I took this from wikipedia. If you check with what ever your likelihood and priors parameters are it probably all works out (you did not add these in the question)  

From a quick google, here's a link to someone going through the proof: link