Question

are all integers also included in real numbers?why?

Answer 1

I expect any number you know about at this stage of your Mathematical learning is a real number: The reals include 
all integers, positive and negative and zero; 
all fractions, positive and negative, including mixed numbers, which of course can be written as improper fractions -- this is the same as saying all numbers which can be written as terminating or recurring decimals; 
all other numbers which can be represented as infinite, non-recurring decimals. 
e.g. pi = 3.14159265 ... continues indefinitely, and never settles down to a repeating pattern. Computers have calculated it to thousands of decimal places. 

Answer 2

real numbers have all the numbers ex:- integers, natural no.s, whole no.s, rational no.s, irrational no.s, etc....
so all integers are also icluded in real numbers