Is this Fundamental Theorem of Calculus?

Calculus Level 2

Let f(x)=0xt(2t+1)2t1dt \displaystyle f(x) = \int_0^x \frac{t(2^t + 1)}{2^t - 1} \, dt .

What is the value of f(1)+f(1)f(1) + f(-1) ?

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