Integral implies reduced and irreducible theorem

Let $X$ be a scheme, and possibly some arrows, satisfying the following conditions:

• $X$ integral

Then

• $X$ irreducible, reduced

References

• Hartshorne, Proposition 3.1 pg 82 (Georgios)
• Stacks Project, https://stacks.math.columbia.edu/tag/01ON (Fabio)