(Solved): I learned the Gram-Schmidt process in turns of projection on the orthogonal vector. Is there any was ...

5. Let $P_1[?1,1]$ denote the real vector space of polynomials of degree not greater than 1 defined on the interval $[?1,1]$, with the inner product $?p,q?={?}_{?1}^{1}p(x)q(x)dx,$ for $p,q?P_1$. Show that the two polynomials $p_1(x)=1+x,p_2(x)=1?x$ are a basis for $P_1[?1,1]$. Use the Gram-Schmidt process to construct an orthonormal basis for $P_1[?1,1]$ from the basis $\left\{p_1,p_2\right\}$.