If you read and understand this appendix on the Riemann integral you will become abnormal if you are not already that way. You will laugh at atrocious puns. You will be unpopular with well adjusted confident people. Furthermore, your confidence will be completely shattered. Virtually nothing will be obvious to you ever again. Consider whether it would be better to accept the superficial presentation given earlier than to attempt to acquire deep understanding of the integral, risking your self esteem and confidence, before proceeding further. This is only here for those who need explanations and are not content to accept on faith.