class MyClass
{
    public:
        MyClass();

        // Note: No longer marked `static`, and only takes the actual argument
        void Callback(int x);
    private:
        int private_x;
};

MyClass::MyClass()
{
    using namespace std::placeholders; // for `_1`

    private_x = 5;
    handler->addHandler(std::bind(&MyClass::Callback, this, _1));
}

void MyClass::Callback(int x)
{
    // No longer needs an explicit `instance` argument,
    // as `this` is set up properly
    cout << x + private_x << endl;
}