Your query is correct except the comma instead of IN keyword must be used.
SELECT POSITION('this is', column1) AS result FROM table;
Also you may use not POSITION but LOCATE function (they are aliases as mentioned in comments)
SELECT LOCATE('this is', column1) AS result FROM table;
or INSTR() function (in this case you must sswap operands)
SELECT INSTR(column1, 'this is') AS result FROM table;
All queries returns positive integer if the substring is found, zero 0 if the substring is not found, and NULL if any operand is NULL.
If you want to return 1/0 output only then you must check what one of these variants is obtained, and convert to needed value. For example,
SELECT CASE WHEN LOCATE('this is', column1)
THEN 1
ELSE 0
END AS result FROM table;
LOCATE('this is', column1) is treated as TRUE returning 1 when the substring is found, and FALSE returning 0 otherwise.
Pay attention - if you use case-sensitive collation then 'this is' substring will not be found in 'This is an example of String' value!
If you need to apply case-insensitive search then you may specify case-insensitive collation explicitly, or apply a function which converts all symbols to lower or upper case (of course, literals does not need in this, they can be printed in needed case). For example,
SELECT LOCATE('this is', LOWER(column1)) AS result FROM table;