integration by parts in Sobolev space $W^{1,1}(mathbb R^d)$

Let $f,gin W^{1,1}(mathbb R^d)$ such that:
$$ int_{mathbb R^d}|nabla f|,|g|,<infty,,quad int_{mathbb R^d}|f|,|nabla g| <infty ,.$$
Can I say that:
$$ int_{mathbb R^d} nabla!f g ,=, -int_{mathbb R^d} f;nabla g quad?$$
I remember this holds true if $f,gin W^{1,2}(mathbb R^d)$. Can this hypothesis be replaced by my weaker hypothesis?