F(x,y) is defined by the integral:

Express F(x,y) as a function of x and y, eliminating the integral sign.

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My approach:

I found the curl of the function to be zero, which means it is path independent and that a potential function exists... I'm now working towards building f from F and finally calculating f(x,y)-f(2,pi)

Which I did and I got:

which means the final value for the integral is:

Does my answer seem correct to you?