Cohomology with compact support of a closed subspace

Question

Let $Y$ be a closed subset of a topological space $X$, let $\mathcal{F}$ be a sheaf on $Y$ and let $j:Y\rightarrow X$ be the inclusion. How to prove that $H_c^i(Y,\mathcal{F})=H_c^i(X,j_*\mathcal{F})$?