Evaluate the definite integrals`int_0^pi(sin^2(x/2)-cos^2(x/2))dx`

Explanation

To evaluate the definite integral

\[ \int_0^{\pi} \left( \sin^2\left(\frac{x}{2}\right) - \cos^2\left(\frac{x}{2}\right) \right) dx, \]

we will follow these steps:

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