How to find the anti-derivative of $\sin^2(x)$?

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I already know that this problem can be solved through a trigonometric identity. However, since this is a relatively simple expression, why can’t the antiderivative just be traced back? In such case, the antiderivative would be $\frac{\sin(x)^3}{3 \cos(x)}$. I am aware that this function will be non continuous at certain points. But would it be a valid anti derivative in certain intervals?