I don't really understand the question but you can try this:
Manipulate[Plot[{Sin[x], Sin[x] Boole[x < y]}, {x, 0, Pi}, Filling -> 2 -> Axis, Frame -> True, ImageSize -> 500, Epilog -> Inset[NIntegrate[Sin[x], {x, 0, y}], {y, 1/2 Sin[y]}, {Right, Center}]], {y, 0, Pi}]