Answer:
[tex]\int _{\left(-1\right)}^1\frac{x^3+1}{2}dx[/tex]
[tex]=\frac{1}{2}\cdot \int _{\left(-1\right)}^1x^3+1dx \Leftarrow(take \: constant\: out)[/tex]
[tex]=\frac{1}{2}\left(\int _{\left(-1\right)}^1x^3dx+\int _{\left(-1\right)}^11dx\right) \Longleftarrow (Sum\:Rule)[/tex]
[tex]\int _{\left(-1\right)}^1x^3dx=0[/tex]
[tex]\int _{\left(-1\right)}^11dx=2[/tex]
[tex]=\frac{1}{2}\left(0+2\right)[/tex]
[tex]=1[/tex]
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