Global.asax

public class WebApiApplication : System.Web.HttpApplication
{
    protected void Application_Start()
    {
        // *** Other Configurations ***
        
        UnityConfiguration(GlobalConfiguration.Configuration);
    }

    public void UnityConfiguration(HttpConfiguration httpConfiguration)
    {
        IUnityContainer container = new UnityContainer();

        container.RegisterType(typeof(IExample), typeof(Example));
        container.RegisterType(typeof (IOtherExample), typeof (OtherExample));
        
        httpConfiguration.DependencyResolver = new IoCContainer(container);
    }
}

IoCContainer.cs

public class IoCContainer : ScopeContainer, IDependencyResolver
{
    public IoCContainer(IUnityContainer container)
        : base(container)
    {
    }

    public IDependencyScope BeginScope()
    {
        var child = container.CreateChildContainer();
        return new ScopeContainer(child);
    }
}

ScopeContainer.cs

public class ScopeContainer : IDependencyScope
{
    protected IUnityContainer container;

    public ScopeContainer(IUnityContainer container)
    {
        if (container == null)
        {
            throw new ArgumentNullException("container");
        }
        this.container = container;
    }

    public object GetService(Type serviceType)
    {
        if (container.IsRegistered(serviceType))
        {
            return container.Resolve(serviceType);
        }
        else
        {
            return null;
        }
    }

    public IEnumerable<object> GetServices(Type serviceType)
    {
        if (container.IsRegistered(serviceType))
        {
            return container.ResolveAll(serviceType);
        }
        else
        {
            return new List<object>();
        }
    }

    public void Dispose()
    {
        container.Dispose();
    }
}