Help with this integral: $\int_{0}^{1}\frac{1}{1+x^{2}}dx$ (Riemann) I'm stuck when I try to solve this integral:
$$\int_{0}^{1}\frac{1}{1+x^{2}}dx$$
I try this:
$$\int_{0}^{1}\frac{1}{1+x^{2}}dx=\lim_{n\rightarrow\infty}\sum_{i=1}^{n}\frac{1}{1+(\frac{i}{n})^{2}}\frac{1}{n}=\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{i=1}^{n}\frac{1}{1+(\frac{i}{n})^{2}}$$
Can someone help with the next step? I'm stuck.

Not sure why you can't use the well-known antiderivative  $arctanx$, to get $$\int_0^1\frac1 {1+x^2}dx=[arctanx]_0^1=\frac \pi4-0=\frac \pi4$$...
