unzip -l archive.zip lists the contents of a ZIP archive to ensure your file is inside.
-p option to write the contents of named files to stdout (screen) without having to uncompress the entire archive.
unzip -p archive.zip file1.txt | less
For this kind of operation I always pipe the output to
less, otherwise the whole file goes flying up the screen before you can read it.
BTW zcat is great for viewing the contents of .gz files without having to uncompress them first.
Edit: Changed this answer to use
-p instead of
-p extracts the file byte-for-byte, while
-c prints the filename and may do EOL conversion. Also,
unzip -p lets you extract multiple files, but it does not output in the order given like