my $dbh = DBI->connect( "dbi:SQLite:$db" ) || warn "Cannot connect: $DBI::errstr";

    my $all = $dbh->selectall_arrayref( "SELECT * from table_X" );

    if ( defined $all ) {

	# table exists
    }
    else {
	# table deosn't exist
    }

    $dbh->disconnect;