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FastSum is specifically designed to compute checksums to ensure file integrity, and it primarily uses the MD5 algorithm for this purpose. MD5 is recognized for its speed and efficiency when generating checksums, making it quite popular in various applications, including file verification. Although MD5 is not the most secure algorithm for cryptographic purposes due to vulnerabilities that can be exploited, it remains effective for integrity checking in many contexts.

The other algorithms listed have distinct contexts and applications. For example, SHA-1 is more secure than MD5 but slower in performance, which isn't as ideal for a tool focused on rapid checksum generation like FastSum. CRC32 is more about error-checking in data transmission rather than generating a strong file integrity checksum, while SHA-256, although very secure, is computationally heavier and not typically associated with FastSum's primary functionality. Therefore, MD5 is the correct answer as it aligns with the FastSum program's intended use for quickly calculating file integrity checksums.