Consider the INTEGRAL (1/t) dt on [1, x]; so f(t) is 1/t. The fundamental theorem of calculus then says:

If F is the antiderivative of f, then the definite integral is equal to

F(x) - F(1) = ln x - ln 1 = ln x

So ln x = INTEGRAL (1/t) dt on [1, x].

The ln yx is a bit confusing. Could that be a typo?