13. [-/1 Points] DETAILS SCALC9 4.4.023.
MY NOTES
Evaluate the definite integral.
\[
\int_{-2}^{3}\left(x^{2}-3\right) d x
\]
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Answer

The definite integral of \(x^{2}-3\) from -2 to 3 is \(\boxed{-\frac{10}{3}}\)

Steps

Step 1 ：Given the definite integral \(\int_{-2}^{3}\left(x^{2}-3\right) d x\)

Step 2 ：The antiderivative of \(x^{2}\) is \(\frac{1}{3}x^{3}\) and the antiderivative of -3 is -3x

Step 3 ：So, the antiderivative of the function is \(\frac{1}{3}x^{3}-3x\)

Step 4 ：We need to evaluate this antiderivative at 3 and -2 and subtract the two results

Step 5 ：The definite integral of \(x^{2}-3\) from -2 to 3 is \(\boxed{-\frac{10}{3}}\)