What is the syntax for the definte integral

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Do you mean the LaTeX syntax? If so, rather than explain the syntax, I'll just create the script that renders in a browser as a definite integral. Double-click it and you can see what I did.

[tex]\int_{0}^{\pi} \frac{sin^2(x)}{3} dx[/tex]

If that's not what you're asking, you'll need to be more clear.