Howto add another test source folder to Maven and compile it to a separate folder?

Based what you’ve written it sounds like you didn’t named your integration tests correctly and you didn’t use the maven-failsafe-plugin for your integration tests. Based on the convention of the maven-failsafe-plugin you should name your integration tests like *IT.java. If you named your integration tests appropriately you can handle that with a more or less configuration like this:

<project ...>
  [...]
  <build>
    [...]
     <plugin>
        <groupId>org.codehaus.mojo</groupId>
        <artifactId>build-helper-maven-plugin</artifactId>
        <version>1.9.1</version>
        <executions>
          <execution>
            <id>add-test-source</id>
            <phase>generate-test-sources</phase>
            <goals>
              <goal>add-test-source</goal>
            </goals>
            <configuration>
              <sources>
                <source>src/integration/java</source>
              </sources>
            </configuration>
          </execution>
        </executions>
      </plugin>
      [...]
  </build>
  [...]
</project>

With the above it’s possible to hold the integration tests within the same module. But this will not solve the idea of having the compiled integration tests classes into a separate folder.

Sometimes it’s better to have a separate integration test module which contains only the integration tests (which results in having a multi-module build).
If you like to leave the conventions of Maven you can try to configure the maven-compiler-plugin to use a different output path (eg. target/integration-tests/classes) which don’t think will really work.