This is surely harder than ever !!!!!!

Algebra Level 5

The function f(x)f(x) is such that f(x)+f(x1)=x2f(x)+f(x-1)= x^{2} If f(19)f(19)=9494. Then find the value of

f(19)+f(20)+f(21)++f(101)f(19) + f(20) + f(21) + \ldots + f(101)

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