try this

package.json

@@ -64,7 +64,7 @@
     "test": "npm run test:tsc && npm run test:unit",
     "test:tsc": "tsc",
     "test:unit": "karma start test/karma.conf.js",
-    "test:integration": "node test/integration/full/test-webdriver.js",
+    "test:integration": "start-server-and-test 'npm run start -- --silent' 9876 'node test/integration/full/test-webdriver.js'",
     "test:examples": "node ./doc/examples/test-examples",
     "test:locales": "mocha test/test-locales.js",
     "test:rule-help-version": "mocha test/test-rule-help-version.js",
@@ -131,6 +131,7 @@
     "sinon": "^7.5.0",
     "sri-toolbox": "^0.2.0",
     "standard-version": "^9.0.0",
+    "start-server-and-test": "^1.11.6",
     "typedarray": "^0.0.6",
     "typescript": "^3.5.3",
     "uglify-js": "^3.4.4",

test/integration/full/test-webdriver.js

@@ -5,14 +5,9 @@ var WebDriver = require('selenium-webdriver');
 var chrome = require('selenium-webdriver/chrome');
 var chromedriver = require('chromedriver');
 var isCI = require('is-ci');
-var execa = require('execa');
 
 var args = process.argv.slice(2);
 
-// start local server in the background
-var startServer = execa('npm', ['run', 'start']);
-startServer.stdout.pipe(process.stdout);
-
 // allow running certain browsers through command line args
 // (only one browser supported, run multiple times for more browsers)
 var browser = 'chrome';
@@ -163,9 +158,6 @@ function buildWebDriver(browser) {
   };
 }
 
-/**
- * Start the integration tests
- */
 function start(options) {
   var driver;
   var isMobile = false;
@@ -241,19 +233,4 @@ function start(options) {
     });
 }
 
-// start the test once the sever is started
-startServer.stdout.on('data', function(chunk) {
-  var str = chunk.toString();
-
-  // NOTE: this is specific from http-server. if we change the
-  // local server we will need to update this to match the
-  // server start output
-  if (str.includes('Starting up')) {
-    // give enough time to finish the startup before starting
-    // test
-    setTimeout(function() {
-      console.log('\nStarting integration test\n');
-      start({ browser: browser });
-    }, 500);
-  }
-});
+start({ browser: browser });