How does cut with breaks work in R

Question

I've tried using?cut but haven't been able to figure out how cut in R works. I'm attempting to grasp how cut divides and makes intervals.
Herein lies my issue:

set.seed(111)
data1 – seq (1, 10, by = 1)
data1 [1] 1 2 3 4 5 6 7 8 9 10
cut(data1, labels = FALSE, breaks = c(0,1,2,3,5,7,8,10)) data1cut
data1cut\s[1] 1 2 3 4 4 5 5 6 7 7
1. Why were 8,9, and 10 left out of the data1cut results?
2. Why do the results of summary(data1) and summary(data1cut) differ?

summary(data1)
Minimum, First Quarter, Median, Third Quarter, Maximum 1.00 3.25 5.50 5.50 7.75 10.00

summary(data1cut)
Minimum, First Quarter, Median, Third Quarter, Maximum 1.00 3.25 4.50 4.40 5.75 7.00
How can I utilise cut more effectively to make, say, 4 bins?