Fixing a commit mistake can be done in two ways. Revert the commit, make the changes and then recommit them. This is the preferred way if we have already made the changes public (and thus someone may already have pulled them). However, in my case I am the only one working on this project right now and I had not pushed the changes to GitHub, so I could try the other method.
So here's what I did. I made changes to the file, added it to the index, and committed it thus:
$git commit --amend
Committing code with the --amend switch will cause the index to be committed as part of the previous commit. Git also brings up the editor window, in case we want to change the commit message. This method can also be used to change the commit message without adding any files to the commit.