public void Configure(IApplicationBuilder app)
{
    app.UseMvc(); // you don't need this
}

public void Configure(IApplicationBuilder app)
{
    app.Map("/api", HandleMapApi);
    // notice how we don't have app.UseMvc()?
}

private static void HandleMapApi(IApplicationBuilder app)
{
    app.Run(async context =>
    {
        // implement your own response
        await context.Response.WriteAsync("Hello WebAPI!");
    });
}

var builder = services.AddMvcCore();

builder.AddViews();
builder.AddRazorViewEngine();
builder.AddRazorPages();

public void ConfigureServices(IServiceCollection services)
{
    // Build a customized MVC implementation, without using the default AddMvc(),
    // instead use AddMvcCore(). The repository link is below:
    // https://github.com/aspnet/Mvc/blob/dev/src/Microsoft.AspNetCore.Mvc/MvcServiceCollectionExtensions.cs

    services
        .AddMvcCore(options =>
        {
            options.RequireHttpsPermanent = true; // this does not affect api requests
            options.RespectBrowserAcceptHeader = true; // false by default
            //options.OutputFormatters.RemoveType<HttpNoContentOutputFormatter>();

            // these two are here to show you where to include custom formatters
            options.OutputFormatters.Add(new CustomOutputFormatter());
            options.InputFormatters.Add(new CustomInputFormatter());
        })
        //.AddApiExplorer()
        //.AddAuthorization()
        .AddFormatterMappings()
        //.AddCacheTagHelper()
        //.AddDataAnnotations()
        //.AddCors()
        .AddJsonFormatters();
}