(C) Given integral is $I = \int \frac{x^3-x^2+x-1}{x-1} dx$. Factorize the numerator: $x^3-x^2+x-1 = x^2(x-1) + 1(x-1) = (x^2+1)(x-1)$. Substitute thi

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(C) Given integral is $I = \int \frac{x^3-x^2+x-1}{x-1} dx$. Factorize the numerator: $x^3-x^2+x-1 = x^2(x-1) + 1(x-1) = (x^2+1)(x-1)$. Substitute this into the integral: $I = \int \frac{(x^2+1)(x-1)}{x-1} dx$. Cancel the common term $(x-1)$: $I = \int (x^2+1) dx$. Integrate term by term: $I = \frac{x^3}{3} + x + C$.