How to write integration tests for net/http based code?

Here is an example code:

package main

import (
	"net/http"
)

func Home(w http.ResponseWriter, r *http.Request) {
	w.Write([]byte("Hello, world!"))
}

func Router() *http.ServeMux {
	mux := http.NewServeMux()
	mux.HandleFunc("/", Home)
	return mux
}

func main() {
	mux := Router()
	http.ListenAndServe(":8080", mux)
}

This is the test case I wrote:

package main

import (
	"net/http"
	"net/http/httptest"
	"testing"
)

func TestMain(t *testing.T) {
	w := httptest.NewRecorder()
	r, _ := http.NewRequest("GET", "/", nil)
	Router().ServeHTTP(w, r)
	if w.Body.String() != "Hello, world!" {
		t.Error("Wrong content:", w.Body.String())
	}
}

Is this test really sending an HTTP request through a TCP socket and reaching the end point /? Or this is just calling the function without making an HTTP connection?

Update

Based on the answer given by @ffk I wrote the test like this:

func TestMain(t *testing.T) {
	ts := httptest.NewServer(Router())
	defer ts.Close()
	req, _ := http.NewRequest("GET", ts.URL+"/", nil)
	client := http.Client{}
	resp, _ := client.Do(req)
	defer resp.Body.Close()
	body, _ := ioutil.ReadAll(resp.Body)
	if string(body) != "Hello, world!" {
		t.Error("Wrong content:", string(body))
	}
}

If you want to instantiate a test server accessible over a random tcp port on 127.0.0.1, use the following:

httpHandler := getHttpHandler() // of type http.Handler
testServer := httptest.NewServer(httpHandler)
defer testServer.Close()
request, err := http.NewRequest("GET", testServer.URL+"/my/url", nil)
client := http.Client{}
response, err := client.Do(request)

For more info, see https://golang.org/pkg/net/http/httptest/#NewServer