Question
Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus. Discuss whether your result is consistent with the figure.$$\int_{0}^{1}\left(x^{2}-2 x+3\right) d x$$
Step 1
The antiderivative of \(x^{2}\) is \(\frac{1}{3}x^{3}\), the antiderivative of \(-2x\) is \(-x^{2}\), and the antiderivative of \(3\) is \(3x\). So, the antiderivative of the function \(x^{2}-2x+3\) is \(\frac{1}{3}x^{3}-x^{2}+3x\). Show more…
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