## Thomas' Calculus 13th Edition

$f(x)=2x-2$
The function $f(x)$ is the derivative of $\int_1^{x} f(t) dt=x^2-2x+1$ by the fundamental Theorem of calculus. This implies that $\int_1^{x} f(t) dt=x^2-2x+1$ $\implies f(x)=2x-2$