Final answer:
Dupin concludes that the speaker was the murderer.
Step-by-step explanation:
In sentences 32-37, Dupin concludes that the speaker was the murderer. This can be inferred from Dupin's mention of a desperate man and a man of nerve, and his hotel with attendants devoted to his interests, indicating someone capable of committing a crime. Additionally, Dupin mentions his political prepossessions, suggesting he has a particular interest in proving the speaker's guilt. Therefore, Dupin's conclusion is that the speaker is the culprit.