How do you numerically integrate the following loss function with respect to $\Phi(f_t)$, given $N_t=50$, $d_t=0$, $\rho=0.2$ and $\pi=0.01$?
$P(D_t=d_t)=\bigl(\begin{smallmatrix} N_T \\ d_t \end{smallmatrix}\bigr)\int\limits_{-10}^{10} \lambda(f_t)^{d_t} \cdot (1-\lambda(f_t))^{N_t-d_t} \text{ }d\Phi(f_t)$ ,with $\lambda(f_t)=P(D_{i,t}=1|F_t=f_t)=\Phi\left(\frac{\Phi^{-1}(\pi)-\sqrt{\rho}f_t}{\sqrt{1-\rho}}\right)$.
Using the following R code, I obtain 4.803584 which is not a valid solution because $P(D_t=0)\in[0,1]$. How can I solve this numerically to get a valid solution?
d<-0; N<-50; rho<-0.2; pd<-0.01; integrand <- function(x) {pnorm(qnorm(pd),mean=sqrt(rho)*x,sd=sqrt(1-rho))}; integrate(integrand, lower = -10, upper = 10)