Evaluate the following definite integral: `int_0^1 1/(1+x^2)dx`

Explanation

Let `I=\int_{0}^{1} \frac{d x}{1+x^{2}}`


`
\Rightarrow \int \frac{d x}{1+x^{2}}=\tan ^{-1} x=F(x)
`


`I=F(1)-F(0)`
`
=\tan ^{-1}(1)-\tan ^{-1}(0)=\frac{\pi}{4}
`