1. A method of ensuring data integrity in a dispersed data storage network, the method comprising: calculating a first checksum for a data segment of data; appending the first checksum to the data segment to produce an appended data segment; encoding the appended data segment to produce a set of encoded data slices, wherein each encoded data slice of the set of encoded data slices includes an encoded representation of at least a portion of the first checksum; generating a set of second checksums for the set of encoded data slices; appending the set of second checksums to the set of encoded data slices to produce a set of appended encoded data slices; and transmitting the set of appended encoded data slices to a plurality of storage units for storage therein; when the data segment is to be reconstructed: retrieving from the plurality of storage units a threshold number of appended encoded data slices of the set of appended encoded data slices; extracting the threshold number of second checksums from the threshold number of appended encoded data slices; and verifying accuracy of the threshold number of appended encoded data slices based on the extracted threshold number of second checksums; and when verifying the accuracy of the threshold number of appended encoded data slices indicates that the threshold number of appended encoded data slices includes a corrupted appended encoded data slice therein: retrieving from at least some of the plurality of storage units a sufficient number of appended encoded data slices needed to generate a reconstructed data segment based on the threshold number of appended encoded data slices that includes the corrupted appended encoded data slice; generating the reconstructed data segment using the sufficient number of appended encoded data slices; performing an error correcting information dispersal algorithm on the reconstructed data segment thereby forming a reconstructed set of data slices; calculating a plurality of second checksums for the reconstructed set of data slices; appending the plurality of second checksums respectively to the reconstructed set of data slices thereby forming a reconstructed set of appended encoded data slices; and replacing the corrupted appended encoded data slice with a reconstructed appended encoded data slice of the reconstructed set of appended encoded data slices; and when the accuracy of the threshold number of appended encoded data slices has been verified: decoding the threshold number of appended encoded data slices to recover the appended data segment; extracting the first checksum from the recovered appended data segment; verifying accuracy of the recovered appended data segment based on the first checksum; and when the accuracy of the recovered appended data segment has been verified, providing the recovered appended data segment as a valid data segment.