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Consider the function $g$ that is continuous on the interval $[−10, 10]$ and that $\int_0^{10}g(x)dx=8$. What is $\int_0^{10}[g(x)+2]dx$ equal to?

So I tried just substituting the first function to get $8+2$ to equal $10$, but that's wrong. I really don't know how to proceed from here.

Xander Henderson
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Ayanoria
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    Go through your steps more slowly and you'll be able to catch your mistake. How do you go from the more complicated integral to the simpler one? (AKA what property of integrals can you use?) – Ninad Munshi Jul 24 '20 at 20:32
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    The the other person pointed out, you should revise the properties of a definite integration, especially the one about addition... – UmbQbify Jul 24 '20 at 20:34
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    If $f$ and $g$ are integrable functions, what is $$\int_{a}^{b} [f(x) + g(x)],\mathrm{d}x?$$ Once you can answer this question, I think that you will have the answer to the question posted here. If not, please edit your answer to my question into your post, and explain where you are getting stuck. – Xander Henderson Jul 24 '20 at 20:35
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    ok I'll try then, thanks! – Ayanoria Jul 24 '20 at 20:37
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    Ohh guys I got it! I had to find out how to integrate a constant! Thank you all! – Ayanoria Jul 24 '20 at 20:53

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