Formal integration

I read a note in the wikipedia article on integration that mentioned the formal evaluation of an integral.  The example was informative

\int \limits_0^1 \sqrt{x} dx = \int \limits_0^1 x^{\frac{1}{2}} dx = \int \limits_0^1 d \left(\frac{2}{3} x^{ \frac{3}{2} } \right) = \frac{2}{3}

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