  For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define
nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This
nonlinear integral arises naturally in the Feynman-Kac formula for stochastic
heat equations with random coefficients. We also define iterated nonlinear
integrals.
