y
  ∫ H(n) dn  = H(y)
    0

from the fundamental theorem of calculus we have that

H'(y)=H(y)  now this is that famous differential equation with solution

H(y)=c*e^y

now puting this into the integral equation we get

c*(e^y - 1)=c*e^y

now the only solution is c=0 thus

H(y)=0

and H(10)+H(20)=0