Why integral y range is y = x?

[Ankit006]

I understand the range of x is 0 to 1. But why y range is 0 to y = x?

 

[Dr.Peterson]

I understand the range of x is 0 to 1. But why y range is 0 to y = x?

Because for a given value of x, y varies from the bottom, y=0, to the top, on the line y=x:

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[Steven G]

Look at any one of those strips. The lowest y value is y=0 and the highest y value is y=x. So y goes from 0 to x.