while( <DATA> ) {
  my $in_toc = 1 .. /^={5,}/;
  if( !$in_toc && /^Chapter 2\./ .. /^Chapter 3\./ ) {
    next if /^Chapter \d+\./;
    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 contain a lot of text with at least 100 words and probably somewhere around 1000-5000. 

Chapter 3. Conclusion
This is the conclusion.