Doubt from area

Illustration 9.8 here i have a doubt that why we have taken negative 1/3 for the integral for 0 to 1/3 in which function is (1-x)^2

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In question 2 why shaded area taken as excluded from parabola and equation of line why didnt we take the region between the parabola and equation of line that is my marked region 2 why we took area of region 1

Region 2 is the area bounded by parabola and line
But they have asked area bounded by parabola, the line and the x axis and hence only region 1 is to be considered

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Exercise 1 question 2 and 3

Please help

Are these the answers?

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Pls check...

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Your are correct

Question no 5

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Question no 8 i am getting option a as answer but answer key mentions option b

I think you missed out the region 1

Question 11 i did this but i got wrong answer what wrong did i make

The area which you have written is the area towards the right of the y axis only , you have not considered the area towards the left of y axis

Then how tp find that

Iā€™m getting option C

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Question no 10 answer key says option b as answer but i think its answer for when parabola is y^2=4x and not -4x