Given $f(z) = \begin{cases} z^{2021}+1, & \text{if $z\neq 0$} \\ 2020, & \text{if $z=0$} \end{cases}$
Then $\int_{|z|=1} f(z)= $
Here $|z|=1$ means as region " the closed circle around origin with radius $1$".
I have not done integration of this type of discontinuous complex function. May be this is easy? But please help me to find a way.