Is $\int_{-\infty}^{\infty}f_X(z-y)f_Y(y)dy$ a PDF where $f_x,f_Y$ are both PDFS

Question

Is $(f_X*f_Y)(z)=\int_{-\infty}^{\infty}f_X(z-y)f_Y(y)dy$ a PDF where $f_X,f_Y$ are both PDFS

I know that when $X,Y$ are independent then the formula is a probability convolution funcntion $(f_X*f_Y)(z)$.

But when $X,Y$ are dependent, is this property still true? In other words, can we prove $\int_{-\infty}^{\infty}(f_X*f_Y)(z)dz=1$, I have no idea on how to evaluate this integral.