The correct answer is C, Amazon Comprehend. This service employs natural language processing (NLP) and machine learning to analyze text and extract insights, including sentiment analysis. It is specifically designed to determine the sentiment of text, making it the ideal choice for analyzing customer service emails to identify whether the engagement was positive or negative. The other options are not suitable for this task: A (Amazon Textract) is for document text extraction, B (Amazon Translate) is for language translation, and D (Amazon Rekognition) is for image and video analysis.