I think $P(H_i)$ are just your prior belief of the hypotheses, not sure if that is what you try to depict here as I believe the integral you wrote should simply be equal to 1.

For example look at this [R package][1] which lets you specify prior odds for hypotheses/models .

I think most often practitioners assume these are equally likely and calculate Bayes factor as simply the posterior ratio .


  [1]: http://%20https://cran.r-project.org/web/packages/BayesFactor/vignettes/odds_probs.html