Suppose that the pedigree shown in the transparency is for a trait caused by recessive allele. is it possible to infer from the pedigree whether or not I-1 and I-2 are carriers of the allele

As we can see in the pedigree, both of the parents do not possess the trait, but one of the four offspring (marked with red) is expressing the trait.

Since the trait is recessive, the only way that is possible that the parents who do not possess the trait to have the offspring with the trait is that the parents are heterozygous for the trait. Meaning that both of the parents have one dominant allele and one recessive allele.