I would suggest to read up a bit on the syntax. See here.
if (dsnt<0.05) {
wilcox.test(distance[result=='nt'],distance[result=='t'],alternative=c("two.sided"),paired=TRUE)
} else if (dst<0.05) {
wilcox.test(distance[result=='nt'],distance[result=='t'],alternative=c("two.sided"),paired=TRUE)
} else
t.test(distance[result=='nt'],distance[result=='t'],alternative=c("two.sided"),paired=TRUE)