Limits of integration when transforming from Cartesian to Polar coordinates

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I am asked to evaluate the following integral question

The diagram at the bottom left shows how I thought about the integral. The diagram at the bottom right shows the correct region of integration.

Could you explain where I am going wrong? Why does the region suddenly stop at the y-axis? In addition, how is it known that the circle cuts the y and x axis at 1? Surely the intercepts are defined by the radius, a, which is not yet defined?