#!/usr/bin/env perl

use strict;
use warnings;

{
    local $/ = '';

    while (<DATA>) {
        next unless /^Chapter 2/ .. /^Chapter 3/;
        last if /^Chapter 3/;
        print;
    }
}

__DATA__
Table of Contents
Chapter 1. Introduction
Chapter 2. Main
Chapter 3. Conclusion

==============================

Chapter 1. Introduction
This is the introduction preceding Chapter 2.

Chapter 2. Main
This is the text contained in Chapter 2 and will ...

Assume more than one paragraph.

Chapter 3. Conclusion
This is the conclusion.