Doubt from integration

@hari_shankar sir please see this..

@pratyaksh_2019,@azimuddin_2019, @Mayank_2019_1 sir please try this..

This is an old Putnam problem

okk sir can you tell the year if u dont mind.i may see solution..thanks sir.

A convex function is a function whose value at the midpoint of the period is less than AM of end pts of the period.

So graphically the sum of areas of starting 2 units and the last 2 units will always be greater than the area between the middle 4 units as the width on x axis is same on both sides but the height in lhs is greater than rhs one

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@Samrat_2020 please you share your approch.