Doubt on Definite Integrals

Problem from black book.

(1) Find the maximum value of \displaystyle \int^{y}_{0}\sqrt{x^4+(y-y^2)^2}dx for all 0\leq y\leq 1.

(2) Calculate maximum value of \displaystyle \int^{1}_{0}\bigg(f(x)\bigg)^3dx . Given that -1\leq f(x)\leq 1. and \displaystyle \int^{1}_{0}f(x)dx=0.

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Is it 1/3 for 1 and 1/4 for 2nd ?

Right sir. Can you plz send me solutions. Thanks

Soon I post solution sir !

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Ok sir, Thanks so much Sir.

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