Find the integral. 
Definitions:
Underlying Purpose
The fundamental reason or objective behind an action, strategy, or piece of work.
Negative Feedback
A response mechanism where the output of a system is used to adjust or control its further actions, typically to reduce differences from a desired state.
Feedback
The information given to individuals regarding their performance or behavior, intended to guide future improvements.
System Purpose
The intended goal or function that a system is designed to achieve within a specific context.
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