A necessary and sufficient condition for the integral functional $I(x( \cdot ),y( \cdot )) = \smallint _G f(t,x(t),y(t))d\mu $ to be sequentially lower semicontinuous with respect to some kinds of strong convergence of $x( \cdot )$components and weak convergence of $y( \cdot )$-components is proved. It is shown how many known and new sufficient conditions can be easily derived from this result. Such properties of the integrand as measurability, lower semicontinuity in $(x,y)$ and convexity in y are also discussed. It appears that if $I( \cdot , \cdot )$ is lower semicontinuous then some other integrand $g(t,x,y)$ such that $g(t,x(t),y(t)) = f(t,x(t),y(t))$ a.e. for any measurable $x( \cdot )$, $y( \cdot )$) necessarily has these properties even if integrand f itself fails to satisfy some or any of them.