How to compile JSX with Babel into JavaScript - node.js

Question

I'm trying to compile the very simplest React tutorial using browserify. I've run:
sudo npm install browserify
Then as stated here http://babeljs.io/docs/setup/#browserify
sudo npm install --save-dev babelify
Then I have my file js/script.jsx
var HelloMessage = React.createClass({
render: function() {
return <div>Hello {this.props.name}</div>;
}
});
ReactDOM.render(<HelloMessage name="John" />, mountNode);
And I'm running from the folder
browserify js/script.jsx -t babelify --outfile bundle.js
But then this happens:
djave at djaves-iMac-3 in /Volumes/djave/react
$ browserify js/script.jsx -t babelify --outfile bundle.js
SyntaxError: /Volumes/djave/react/js/script.jsx: Unexpected token (4:11)
2 | var HelloMessage = React.createClass({
3 | render: function() {
> 4 | return <div>Hello {this.props.name}</div>;
| ^
5 | }
6 | });
7 |
What am I doing wrong? This is literally my first step into this area so it may be I've missed a pretty major step.
More errors (although I suspect this won't help too much!)
at Parser.pp.raise (/Volumes/djave/react/node_modules/babelify/node_modules/babel-core/node_modules/babylon/index.js:1425:13)
at Parser.pp.unexpected (/Volumes/djave/react/node_modules/babelify/node_modules/babel-core/node_modules/babylon/index.js:2907:8)
at Parser.pp.parseExprAtom (/Volumes/djave/react/node_modules/babelify/node_modules/babel-core/node_modules/babylon/index.js:754:12)
at Parser.pp.parseExprSubscripts (/Volumes/djave/react/node_modules/babelify/node_modules/babel-core/node_modules/babylon/index.js:509:19)
at Parser.pp.parseMaybeUnary (/Volumes/djave/react/node_modules/babelify/node_modules/babel-core/node_modules/babylon/index.js:489:19)
at Parser.pp.parseExprOps (/Volumes/djave/react/node_modules/babelify/node_modules/babel-core/node_modules/babylon/index.js:420:19)

Answer 1

All fixed, thanks to #azium.
First get the React preset: http://babeljs.io/docs/plugins/preset-react/
npm install babel-preset-react
Next, create a file called .babelrc in the root of your project, and put in it the following:
{
"presets": ["react"]
}
Then do the
browserify js/script.jsx -t babelify --outfile bundle.js
That compiles everything, and as an extra to make sure that react and react-dom are included (as shown here) you can run the following:
sudo npm install --save react react-dom