"we had a busy month to review our lessons? or we had a busy month reviewing our lessons?" what is the difference be tween them?

haw to finish the sentence "we had a busy month +to review ? or + reviewing?" and why? i don't know the difference between an infinitive and a gerund in this sentence.How

Is the sentence right?"The article has many mistakes. In terms of me , I like the movie"

First notebook entry: Introducing myself I want to learn English well, so that I can watch movies in English and comunicate with native people in English. Will you help me?