A question related to Integral and supremum

Question

Let $f\in L_{p}([0,1])$ and 1-periodic on $R^{1}.$ Suppose $[a,c]\subset [0,1].$ Are the following quantities equal? $$ \underset{|h|\leq \delta_{1}}{\sup}\int_{a}^{b}|f(x+h)-f(x)|^{p}dx+ \underset{|h|\leq \delta_{2}}{\sup}\int_{b}^{c}|f(x+h)-f(x)|^{p}dx $$ and $$ \underset{|h|\leq \max\{\delta_{1}, \delta_{2}\}}{\sup}\int_{a}^{c}|f(x+h)-f(x)|^{p}dx $$