How do I write that x belongs to the domain of all real numbers R , such that x is greater than or equal to a and less than or equal to b ?

The closed interval [a,b] is the set of all real numbers x such that alt= xlt= b . This is written as,
[a,b]={x in R| alt= xlt= b}
This is usually written this simply as {x | alt= xlt= b} , and it is understood that x belongs to R .
https://www.varsitytutors.com/hotmath/hotmath_help/topics/interval-notation