Remove deprecated Auth function from C++ SDK

auth/integration_test/src/integration_test.cc

@@ -761,18 +761,13 @@ TEST_F(FirebaseAuthTest, TestUpdateEmailAndPassword) {
   firebase::auth::User user = auth_->current_user();
   EXPECT_TRUE(user.is_valid());
 
-  // Update the user's email and password.
-  // const std::string new_email = "new_" + email;
-  // WaitForCompletion(user.UpdateEmail(new_email.c_str()), "UpdateEmail");
+  // Update the user's password.
+  // Email update functionality has been changed and the old UpdateEmail method removed.
+  // A more comprehensive test for the new email update flow
+  // (SendEmailVerificationBeforeUpdatingEmail) would be needed here.
   WaitForCompletion(user.UpdatePassword(kTestPasswordUpdated),
                     "UpdatePassword");
 
-  // firebase::auth::Credential new_email_cred =
-  //     firebase::auth::EmailAuthProvider::GetCredential(new_email.c_str(),
-  //                                                      kTestPasswordUpdated);
-  // WaitForCompletion(user.Reauthenticate(new_email_cred), "Reauthenticate");
-  // EXPECT_TRUE(user.is_valid());
-
   WaitForCompletion(user.SendEmailVerification(), "SendEmailVerification");
   DeleteUser();
 }