Question

Evaluate: ${\int }_{-1}^1(x+1)dx$

Answer 1

$I=\underset{-1}{\overset{1}{\int }}(x+1)dx$

Now, $\int (x+1)dx=\frac{x^2}{2}+x=F\left(x\right)$

Therefore,

$I=\frac{1}{2}+1-(\frac{1}{2}-1)=2$