Is one who misses Fajr prayer by one minute due to oversight sinful, and is his prayer considered a makeup prayer?

If you pronounce the takbirat al-ihram before the time expires and prolong the prayer until the time has elapsed, then if you complete one rak'ah before sunrise, you have performed the prayer on time (ada'an). If you complete less than one rak'ah, there is a difference of opinion; some scholars hold that the prayer is considered performed on time even if only the takbirat al-ihram is pronounced within the time.

The Malikis are of the view that completing a part of the prayer within its prescribed time renders it a timely performance. The disagreement revolves around whether this part must be one rak'ah or more, or less than that. There is no sin in prolonging the prayer until its time has elapsed, as long as it was commenced within its time.