diff --git a/integration-tests/hibernate-search-elasticsearch/README.md b/integration-tests/hibernate-search-elasticsearch/README.md
index 47f7e02fe25e8..4ecf385695306 100644
--- a/integration-tests/hibernate-search-elasticsearch/README.md
+++ b/integration-tests/hibernate-search-elasticsearch/README.md
@@ -1,10 +1,10 @@
-# Hibernate Search example with ElasticSearch
+# Hibernate Search example with Elasticsearch
 
 ## Running the tests
 
 By default, the tests of this module are disabled.
 
-To run the tests in a standard JVM with ElasticSearch started in the JVM, you can run the following command:
+To run the tests in a standard JVM with Elasticsearch started in the JVM, you can run the following command:
 
 ```
 mvn clean install -Dtest-elasticsearch
diff --git a/integration-tests/reactive-mysql-client/README.md b/integration-tests/reactive-mysql-client/README.md
index ad87f139c368f..c5cbdc5981f6d 100644
--- a/integration-tests/reactive-mysql-client/README.md
+++ b/integration-tests/reactive-mysql-client/README.md
@@ -4,7 +4,7 @@
 
 By default, the tests of this module are disabled.
 
-To run the tests in a standard JVM with MySQL started as a Docker container, you can run the following command:
+To run the tests in a standard JVM with MariaDB started as a Docker container, you can run the following command:
 
 ```
 mvn clean install -Dtest-mariadb -Ddocker
@@ -16,7 +16,7 @@ Additionally, you can generate a native image and run the tests for this native
 mvn clean install -Dtest-mariadb -Ddocker -Dnative
 ```
 
-If you don't want to run MySQL as a Docker container, you can start your own MySQL server. It needs to listen on the default port and have a database called `hibernate_orm_test` accessible to the user `hibernate_orm_test` with the password `hibernate_orm_test`.
+If you don't want to run MariaDB as a Docker container, you can start your own MariaDB or MySQL server. It needs to listen on the default port and have a database called `hibernate_orm_test` accessible to the user `hibernate_orm_test` with the password `hibernate_orm_test`.
 
 You can then run the tests as follows (either with `-Dnative` or not):