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Checking Perfect Square by Unit Digit

Integrate: dx...

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Integrate: dx/a square+x square

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If we convert the denominator of the integral into a perfect square, $\int \frac{1}{x^{2} - x + 1} d x$ then the correct integral will be

Q. Value of the integral

\oint_{c} (x y d y - y^{2} d x)

, where C is the square cut from the first quadrant by the lines x = 1 and y = 1 will be (use Green's theorem to change the line integral into double integral)

Q. If we convert the denominator of the integral into a perfect square,

\int \frac{1}{x^{2} - x + 1}

dx then the correct integral will be

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