Answer:
[tex]\frac{4}{3(e^2+1)}[/tex]
Step-by-step explanation:
We want to evaluate:
[tex]\int\limits^1_{-1} {\frac{x^2+1}{e^2+1} } \, dx[/tex]
This is the same as:
[tex]\frac{2}{e^2+1} \int\limits^1_{0} {x^2+1} \, dx[/tex]
We integrate to obtain:
[tex]\frac{2}{e^2+1} (\frac{x^3}{3}+x)|_0^1[/tex]
We evaluate to obtain:
[tex]\frac{2}{e^2+1} (\frac{1^3}{3}+1)=\frac{4}{3(e^2+1)}[/tex]
