f = Sin[2*x];

Plot[f, {x, 0, 10}]

c = (∫_0^10) f (x)*
          f (x + y) \[DifferentialD]x

Plot[c, {y, 0, 10}]

Plot[f*f /. x -> x + 0.8, {x, 0, 10}]

Plot[f /. x -> x + 1, {x, 0, 10}]