In　terms　of　a　mathematical　expression　of　the　quantitative　causal　principle,　this　paper　gives　a　unification　of　Hamilton,　Voss,　Holder,　Maupertuis-Lagrange　variational　principles　of　integral　style　of　the　second-order　Lagrangians,　and　finds　the　intrinsic　relations　among　all　the　different　integral　variational　principles.　It　is　proved　that　f(0)　=　0　is　just　the　result　satisfying　the　quantitative　causal　principle.　The　Noether　conservation　charges　of　Hamilton,　Voss,　Holder,　Maupertuis-Lagrange　variational　principles　are　shown　up,　and　the　intrinsic　relations　among　the　Noether　conservation　charges　of　all　the　integral　variational　principles　are　discovered.　Our　investigations　make　the　expressions　of　the　past　scrappy　numerous　variational　principles　be　unified　into　a　relative　consistent　system　of　all　the　variational　principles　in　terms　of　the　quantitative　causal　principle,　and　show　that　all　the　variational　principles　become　deductions　of　the　quantitative　causal　principle.