Say I have two strings,
String s1 = "AbBaCca";
String s2 = "bac";
Yes, contains is case sensitive. You can use java.util.regex.Pattern with the CASE_INSENSITIVE flag for case insensitive matching:
EDIT: If s2 contains regex special characters (of which there are many) it's important to quote it first. I've corrected my answer since it is the first one people will see, but vote up Matt Quail's since he pointed this out.