Computing $E[X]$ for $s(x)=(1-x)^n I_{(0,1)}(x)$

Question

Using the right tail formula for expectation:

$$E[X]=\int_0^\infty s(x)dx=\int_0^\infty(1-x)^ndx$$

but it diverges, I would like want to know what is my error.

Answer 1

Correction: $$E[X]=\int_0^\infty s(x)dx=\int_0^1(1-x)^ndx+\int_1^\infty 0 dx=\frac{1}{n+1}$$