It depends on how you use the adjective "brief." In the first sentence, "brief" modifies "developing history..." That means a snapshot in time of an ongoing process--history. In the second sentence, "brief" modifies "history of..." Which means a summary of. Grammatically, the first sentence does not make sense since you do not know the duration of an ongoing action/process, therefore you cannot call it brief. For more technical information, search "Using Gerunds & Infinitives." http://www.englishteachermelanie.com/grammar-gerunds-and-infinitives-for-purpose/

"brief developing history of psychology" works but not the best. "brief history of the development of psychology" sounds a lot better than the first one.