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\begin{aligned} \int_0^1 (3x^2 + 2x + 1)\,dx &= \int_0^1 3x^2\,dx + \int_0^1 2x\,dx + \int_0^1 1\,dx \\ &= 3 \cdot \left[\frac{x^3}{3}\right]_0^1 + 2 \cdot \left[\frac{x^2}{2}\right]_0^1 + \left[x\right]_0^1 \\ &= (1) + (1) + (1) = 3 \end{aligned}