How to automate integration testing of Java functions?

<dependency>
  <groupId>junit</groupId>
  <artifactId>junit</artifactId>
  <version>4.13.2</version>
  <scope>test</scope>
</dependency>
<dependency>
  <groupId>org.mockito</groupId>
  <artifactId>mockito-core</artifactId>
  <version>4.6.1</version>
  <scope>test</scope>
</dependency>
<dependency>
  <groupId>com.google.cloud</groupId>
  <artifactId>google-cloud-functions-framework-testing</artifactId>
  <version>3.4.1</version>
  <scope>test</scope>
</dependency>

import static com.google.common.truth.Truth.assertThat;
import static org.mockito.Mockito.when;

import com.google.cloud.functions.HttpRequest;
import com.google.cloud.functions.HttpResponse;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.PrintWriter;
import java.io.StringReader;
import java.nio.charset.StandardCharsets;
import java.util.Map;
import org.junit.Before;
import org.junit.Rule;
import org.junit.Test;
import org.junit.rules.TestRule;
import org.mockito.Mock;
import org.mockito.MockitoAnnotations;

public class ExampleFunctionTest {

  @Rule
  public TestRule FUNCTIONS_FRAMEWORK_TEST_RULE = new FunctionsFrameworkExtensionRule();

  @Mock
  private HttpRequest request;

  @Mock
  private HttpResponse response;

  private BufferedWriter writerOut;
  private PrintWriter printWriter;

  @Before
  public void beforeEach() {
    MockitoAnnotations.initMocks(this);
    writerOut = new BufferedWriter(new PrintWriter(response.getWriter()));
    printWriter = new PrintWriter(writerOut, true);
  }

  @Test
  public void helloHttp_shouldPrintAName() throws IOException {

    // Mock request
    when(request.getReader()).thenReturn(new StringReader("{}"));

    // Invoke function under test
    new ExampleFunction().service(request, response);

    // Assert that the function writes "Hello World!" to the response
    writerOut.flush();
    assertThat(printWriter.toString()).isEqualTo("Hello World!");
  }
}